# Define the word inequality

Size: px
Start display at page:

Transcription

1 Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two Step Inequalities Reminders: Solving Inequalities 1

2 Students can define inequality. Inequality: is like an equation that uses symbols for "less than" (<), "less than or equal to" ( ), "greater than" (>), and "greater than or equal to" ( ) where an equation uses a symbol for "is equal to" (=). Students can explain inequalities. Explain each situation shown on the balance scales using inequalities vocabulary. 2

3 Students can identify symbolic representation of inequalities. Inequality Symbols Less Than < Greater Than > Less Than or Equal Too < Greater Than or Equal Too > Students can identify symbolic representation of inequalities. Inequality Symbols Less Than < Greater Than > Less Than or Equal Too < Greater Than or Equal Too >

4 Students can identify symbolic representation of inequalities. Set Notation: 3 < x < 10 Number line: 3 10 Interval Notation: (3, 10) Students can identify symbolic representation of inequalities. For each of the following in set notation, a. Create a Number Line b. Write in each of the following in Interval Notation 1. x > 2 2. x < x x < 9 4

5 Students can solve one-step linear inequalities with one variable. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. a) x 4 > 9 b) x + 6 < _ 4 Students can solve one-step linear inequalities with one variable. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. x c) x < 4 d) 9x > 36 3 _ 5

6 Students can solve two-step linear inequalities with one variable. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. a) 5x + 3 < _ 4 b) 10x 3 > 7 Students can solve two-step linear inequalities with one variable. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. c) 5x + 3 > 4 d) x < 1 x 5 2 6

7 Students can solve linear inequalities with a negative coefficient. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. _ a) 6x < 12 b) x < 8 When you mulply or divide by a negave number, you MUST switch the inequality sign. Students can solve linear inequalities with a negative coefficient. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. c) 2x + 6 > 8 d) 17 3x > 2 _ When you mulply or divide by a negave number, you MUST switch the inequality sign. 7

8 YOUR TURN!! Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. x a) 4x + 7 > 5 b) 5x 3 > 0 c) x + 9 > 6 x d) x 2 < 5 e) 4x + 1 < 13 f) 4x > 5 x g) 3x < 12 h) 6x + 1 < 0 i) 5x 2 < 17 When you mulply or divide by a negave number, you MUST switch the inequality sign. Warm Up What was done to both sides of the first inequality to give the second in each of the following below? 1) x 7 < 2 to give x < 9 2) 3x > _ 15 to give x > _ 5 3) x + 10 > 0 to give x > 10 4) 6x < 12 to give x > 2 5) x _ < 8 to give x > _ 8 6) x > 1 to give x < 4 4 8

9 Agenda: Do Now Homework Questions Objective Solving inequalities with the Distributive Property Reminders: Algebra Common Core Students can use the distributive property when solving an inequality. Students can explain each step in solving an inequality as following the equality of numbers asserted in the previous step, starting from the assumption that the original inequality has a solution. Students can write solutions to inequalities in interval notation. 9

10 RECALL: ONE STEP TWO STEP x + 4 > 3 5x 13 _ < 2 Students can solve inequalities with the Distributive Property. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. a) 5(x - 2) < 30 b) 3(6 + x) > -36 c) 2(x + 4) < 9-10

11 Students can solve inequalities with the Distributive Property. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. d) 2(4x - 9) - 6x > 0 e) -(x + 7) > 15 f) 5(x - 2) - 4(x - 1) < 0 - Students can solve inequalities with the Distributive Property. YOUR TURN: Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Write a list of these values. Write it in interval notation. a)3(5x + 4) < 42 b) 5x - 2(2x + 1) > 8 c) 4(r + 5 ) -> 8 d) -6(a+2) +7a < 12 e) -(2a - 6) + 3(a + 2) < 4-11

12 Warm Up Amanda has \$40 to spend on flowers. She wants to buy a pair of red roses for \$18 and the rest on lily flowers. Each lily costs \$11. How many lily flowers can she purchase? 11x + 18 _ < 40 Agenda: Do Now Homework questions Objective Solving Inequalities with Variables on Both Sides Reminders: 12

13 Algebra Common Core Students can explain each step in solving an inequality as following the equality of numbers asserted in the previous step, starting from the assumption that the original inequality has a solution. Students can write solutions to inequalities in interval notation. RECALL: ONE STEP TWO STEP DISTRIBUTIVE x > 8 2x + 12 < 4 2x 2(x 1) < 5 _ 4 13

14 Students can solve inequalities with variables on both sides. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a # line representing these values. Write it in interval notation. a) -2m - 27 _ > -5m - 6 b) 9j + 3 < 8j + 4 c) 5p + 10 < _ p Students can solve inequalities with variables on both sides. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a # line representing these values. Write it in interval notation. d) 3m - 2 < _ 5m + 10 e) 5a - 4 < 6a + 4 f) 2 x + 5 _ > 1 x

15 Students can explain each step when solving an inequality. On each line provided, identify the property being used. -6y + 20 < 3y y < 3y y - 3y -9y < y > 3 Subtraction Property of Equality Subtraction Property of Equality Division Property of Equality Students can solve inequalities with variables on both sides. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Write a list of these values. Write it in interval notation. a) 6-6g _ > 8-5g b) 3t + 4 > 4t + 7 c) 6d - 16 _ < -32-2d d) 5w + 8 > 3w + 14 e) 5k + 7 > 8k - 8 f) 2-6 > h 2 h 15

16 Students can explain each step when solving an inequality. On each line provided, identify the property being used. 7u + 8 < u u < 6 + 9u - 9u - 9u -2u < u > -3 Subtraction Property of Equality Subtraction Property of Equality Division Property of Equality Warm Up What was done to both sides of the both sides of the first inequality to give the second of the following? a) x 7 < 2 to give x < 9 b) x < 9 to give x < 18 2 c) 5x 2 < 17 to give 5x < 15 d) 2(x 6) > 3 x to give 2x 12 > 3 x 16

17 Agenda: Do Now Homework Questions Objective Solving Multi Step Inequalities Reminders: Algebra Common Core Students can explain each step in solving an inequality as following the equality of numbers asserted in the previous step, starting from the assumption that the original inequality has a solution. Students can write solutions to inequalities in interval notation. 17

18 RECALL: ONE STEP TWO STEP 7x < _ 28 x _ < 0 DISTRIBUTIVE VARIABLES ON BOTH SIDES 2(x 5) > 30 2x + 15 > 3 + 4x Students can solve inequalities with Multi Steps. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. a) 3(x + 3) < 2(x + 6) b) x + 5 > 3x - 2(x - 1) 18

19 Students can solve inequalities with Multi Steps. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. c) 4a - 3-2(4 - a) < _ 7a - 10 d) 1 2 (4x + 8) < _ 6x + 44 Students can solve inequalities with Multi Steps. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. e) (x - 4)(x + 1) > x(x - 4) 19

20 YOUR TURN Students can solve inequalities with Multi Steps. Solve the following inequalities for x. Explain which values of x make this algebraic sentence true. Draw a number line representing these values. Write it in interval notation. _ a) 2(5p + 10) < 2( p) b) 5 + 7r > -(3-2r) - 3r _ c) 9z - (6 - z) > 12z -10 d) (x + 2)(x - 3) < x(x - 2) e) 1 (3x - 27) > 2(x - 5) 3 Review for Quiz Warm Up 20

21 Warm Up What happens to the direction of an inequality if... a) the same number is subtracted from both sides? b) both sides are multiplied by the same positive number? c) both sides are divided by the same negative number? Agenda: Do Now Objectives Translating an English sentence in an symbolic inequality Reminders: 21

22 Algebra Common Core Obectives: Students can solve word problems that lead to inequalities. Students can explain each step in solving an inequality as following the equality of numbers asserted in the previous step, starting from the assumption that the original inequality has a solution. Students can write solutions to inequalities in interval notation. Students can solve word problems that lead to inequalities. Word Problems Solved by Inequalities Frequently, word problems involve translating an English sentence into an inequality. For example, Tony can spend at most \$25 on a football. This means that he must spend \$25 or less. Therefore, at most is translated as _ <. Janet needs at least a 90 average for all her subjects to quality for the honor roll. This means that she must have an average of 90 or greater. Therefore, at least is translated as _ >. 22

23 Students can solve word problems that lead to inequalities. Example One Jamal is paid \$150 a week plus a commission of \$40 on each stereo he sells. How many must he sell to make at least \$350 a week? STRATEGY Let x = the number he can sell. Think: salary plus commission is at least 350 salary plus number sold times 40 is at least 350 salary plus x 40 is at least x > 350 Solve the translated inequality... Students can solve word problems that lead to inequalities. Example Two Mona rents a care \$ 175 a week, plus \$0.15 a mile. How far can she travel if she wants to spend at most \$250? STRATEGY Let x = the number of miles she can travel. fixed cost + cost per mile number of miles is at most

24 Students can solve word problems that lead to inequalities. Your Turn An amusement park charges \$6 for admission and \$0.70 for each ride. If you go to the park with \$20, what is the maximum number of rides you can go on? 2. You want to start a business making custom t shirts. It will cost you \$48 for supplies. It costs you \$4.50 to make each t shirt which you will sell for \$8.50. Write an inequality showing how many you must sell to earn a profit of at least \$600. Solve. Explain. 3. You and you friends have a total of \$12.50 to spend on pizza. A large pizza with cheese costs \$10, plus \$0.50 for each additional topping. What's the most toppings you can afford? 4. Brian is paid \$150 a week, plus a commission of \$15 on each camera he sells. How many must he sell to make at least \$600 a week? Warm Up Translate the following algebraic inequalities into sentences. a) 10 times a number is at least 60 b) 39 is less than the difference of 21 and a number. 24

25 Agenda: Do Now Objectives Master of Translating: Translating an English sentences and phrases into algebraic expression, equations, and inequality Reminders: Students can solve word problems that lead to inequalities. Students can explain each step in solving an inequality as following the equality of numbers asserted in the previous step, starting from the assumption that the original inequality has a solution. Students can write solutions to inequalities in interval notation. Students can complete Master of Translating. 25

26 Warm Up Graph the function y = 2x + 3 How many regions does the line separate the coordinate plane into? Agenda: Do Now Objectives Graphing Linear Inequalities Reminders: 26

27 Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Graphing the iequality y < 2x + 3 Graphing the inequality y > 2x + 3 Graphing the inequality y < _ 2x + 3 _ Graphing the inequality y > 2x

28 SUMMARY Inequality Symbol Line Shade > Dotted Up < Dotted Down Solid Up Solid Down Graph the inequality: y x 5 Slope? y intercept? Line? Shade? SOLUTIONS: 28

29 Graph the inequality: y < 2x + 1 Slope? y intercept? Line? Shade? SOLUTIONS: Graph the inequality: y < 3x Slope? y intercept? Line? Shade? SOLUTIONS: 29

30 Graph the inequality: y 2x +2 Slope? y intercept? Line? Shade? SOLUTIONS: YOUR TURN 30

31 Warm Up Solve the following inequality for y: 2x 3y < 9 Could the following inequalities be graphed on a coordinate plane? x 6 y > 4 Agenda: Do Now Objectives Graphing Linear Inequalities Practice: Finish Worksheet from yesterday. Reminders: 31

32 Agenda: Do Now Homework Questions Writing linear equations Reminders: 32

33 33

34 Warm Up for THE FOLLOWING linear inequalities, IDENTIFY WHETHER YOU'D HAVE A SOLID OR DOTTED LINE AND IF YOU'D SHADE UP OR DOWN. 1. Y -2X Y < X Y 2 4. Y < 3 5. Y -X - 3 Solving Systems of Linear Inequalities Agenda: Do Now Objectives Graphing Systems of Linear Inequalities Reminders: 34

35 Student's can graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 35

36 36

37 Warm Up The following linear inequalities can't be graphed in their current state. Make them so you can graph them. 1) 4x - 3y 2) 2x + y 2 Nov 25 10:43 AM Student's can graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Nov 25 10:43 AM 37

38 Nov 25 10:43 AM Nov 25 10:43 AM 38

39 Nov 25 10:43 AM Review for Quiz Warm Up 39

40 Agenda: Objective: > Students can determine where a function is increasing and decreasing. > Students can determine the range given a domain of a piecewise function. Reminders: Nov 21 9:43 AM Increasing/ Decreasing Functions A function is increasing when the slope is positive. A function is decreasing when the slope is negative. A function is constant when the slope is 0. Nov 21 9:43 AM 40

41 Increasing/ Decreasing Functions We will use INTERVAL NOTATION or SET NOTATION when we write the intervals of increase and decrease. Intervals of increase or decreae are always CLOSED!!! Where is f(x) increasing? Where is f(x) decreasing? Where is f(x) constant? Nov 21 9:43 AM Increasing/ Decreasing Functions Where is f(x) increasing? Where is f(x) decreasing? Where is f(x) constant? f(x) Nov 21 9:43 AM 41

42 Increasing/ Decreasing Functions Where is f(x) increasing? Where is f(x) decreasing? Where is f(x) constant? f(x) Nov 21 9:43 AM Increasing/ Decreasing Functions Let's take a look at a piecewise function. Remember, a piecewise function is simply a function made up of 2 or more "pieces." These pieces can be linear, quadratic, exponential, etc. You Try: 1. Evaluate h(3). 2. Evaluate h(0) 3. Evaluate h(1). Nov 21 9:43 AM 42

43 Increasing/ Decreasing Functions When you are asked to evaluate a piecewise function at a specific x value, you must use the closed value for the y value. Example: Evaluate: f(x) a. f( 4) b. f(2) c. f( 2) Nov 21 9:43 AM Increasing/ Decreasing Functions Example: Evaluate: a. y(0) b. y(6) c. y(2) Nov 21 9:43 AM 43

44 Increasing/ Decreasing Functions Exit Ticket: Determine where f(x) is increasing and decreasing. Evaluate f(4). Nov 21 9:43 AM Warm UP Given f(x) = 3x 1 and g(x) = 2 + x 2, evaluate the following: 1. f(2) 2. g(2) 3. g( 1) 4. f( 5) 5. g( 3) Nov 21 2:33 PM 44

45 Agenda: Objective: > Students can determine where a function is increasing and decreasing. > Students can determine the range given a domain of a piecewise function. Reminders: Nov 21 2:33 PM Increasing/ Decreasing Functions Class Work: In pairs or independently, please complete the following problems. Please hand this in before class ends. If you finish, please let me know and I have Quick Checks for you to work on for extra credit. Nov 21 9:43 AM 45

46 Increasing/ Decreasing Functions 1. Determine the intervals of increase and decrease for each function given. 2. Evaluate: a. f(0) b. f(1) Pay attention to the scale on the graph! Nov 21 9:43 AM Increasing/ Decreasing Functions 3. Determine the intervals of increase and decrease for each function given. 4. Evaluate: a. f( 1) b. f(1) Pay attention to the scale on the graph! Nov 21 9:43 AM 46

47 Increasing/ Decreasing Functions 5. Determine the intervals of increase and decrease for each function given. 6. Evaluate: a. f(0) b. f(1) Pay attention to the scale on the graph! Nov 21 9:43 AM Increasing/ Decreasing Functions BONUS (+5 on your next quiz!) *Choose an appropriate scale! Nov 21 9:43 AM 47

48 Do NOW: Review Agenda: Reminders: 48

### Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations. Unit Calendar

Algebra 1 Spencer Unit 4 Notes: Inequalities and Graphing Linear Equations Unit Calendar Date Topic Homework Nov 5 (A ) 6.1 Solving Linear Inequalities +/- 6.2 Solving Linear Inequalities x/ 6.3 Solving

### UNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:

UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities

### Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities

Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,

### Chapter 6 Solving and Graphing Linear Inequalities

Chapter 6 Solving and Graphing Linear Inequalities 6.1 Solving Inequalities in One Variable: The graph of a linear inequality in one variable is the line of of the inequality on the real number The four

### Section 2.2 Objectives

Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational

### Algebra I Solving & Graphing Inequalities

Slide 1 / 182 Slide 2 / 182 Algebra I Solving & Graphing Inequalities 2016-01-11 www.njctl.org Slide 3 / 182 Table of Contents Simple Inequalities Addition/Subtraction click on the topic to go to that

### Indiana Core 40 End-of-Course Assessment Algebra I Blueprint*

Types of items on the Algebra I End-of-Course Assessment: Multiple-choice 1 point per problem The answer to the question can be found in one of four answer choices provided. Numeric response 1 point per

### Solving and Graphing Linear Inequalities Chapter Questions. 2. Explain the steps to graphing an inequality on a number line.

Solving and Graphing Linear Inequalities Chapter Questions 1. How do we translate a statement into an inequality? 2. Explain the steps to graphing an inequality on a number line. 3. How is solving an inequality

### LHS Algebra Pre-Test

Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well

### UNIT 2 SOLVING EQUATIONS

UNIT 2 SOLVING EQUATIONS NAME: GRADE: TEACHER: Ms. Schmidt _ Solving One and Two Step Equations The goal of solving equations is to. We do so by using. *Remember, whatever you to do one side of an equation.

### Name: Date: Period: Notes Day 2 Inequalities Vocabulary & Interval Notation

Name: Date: Period: Notes Day 2 Inequalities Vocabulary Interval Notation Interval Notation: Start at the point and end at the point. The smallest number possible is and the largest is. To indicate that

### Inequalities Chapter Test

Inequalities Chapter Test Part 1: For questions 1-9, circle the answer that best answers the question. 1. Which graph best represents the solution of 8 4x < 4 A. B. C. D. 2. Which of the following inequalities

### CRS SKILL LEVEL DESCRIPTION

GRE 501 LESSON/NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must GRE 301 Locate points on the number line attain mastery at this level R- XEI 506 Solve first degree inequalities that

### Unit 7 Systems and Linear Programming

Unit 7 Systems and Linear Programming PREREQUISITE SKILLS: students should be able to solve linear equations students should be able to graph linear equations students should be able to create linear equations

### Algebra 1 ECA Remediation Diagnostic Homework Review #1

Algebra 1 ECA Remediation Diagnostic Homework Review #1 Lesson 1 1. Simplify the expression. 8 5(7 r) A1.1.3.1 Lesson. Solve the equation. 4x 1 = 9 x A1..1 Lesson 3. Solve the equation. 1.6n 5.95 = 11.7

### Algebra I Notes Linear Inequalities in One Variable and Unit 3 Absolute Value Equations and Inequalities

PREREQUISITE SKILLS: students must have a clear understanding of signed numbers and their operations students must understand meaning of operations and how they relate to one another students must be able

### 1 st : Read carefully and underline key words 2 nd : Write a let statement 3 rd : Determine whether to use,,, or 4 th : Write and solve the inequality

Name Period: Represent each of the following as an algebraic inequality. 1) x is at most 30 2) the sum of 5x and 2x is at least 14 3) the product of x and y is less than or equal to 4 4) 5 less than a

### Topic 1. Solving Equations and Inequalities 1. Solve the following equation

Topic 1. Solving Equations and Inequalities 1. Solve the following equation Algebraically 2( x 3) = 12 Graphically 2( x 3) = 12 2. Solve the following equations algebraically a. 5w 15 2w = 2(w 5) b. 1

### Solving Equations Quick Reference

Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number

### 8 th Grade Algebra 1 (Honors) Subject

Subject Nine Week Standard 8 th Grade Algebra 1 (Honors) First 9 Weeks Standards are not covered in their entirety during this 9 weeks. Standards will be repeated throughout the course. N-Q.A.1: Use units

### Name Period Date DRAFT

Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,

### Algebra 1 ECA Remediation Diagnostic Homework Review #2

Lesson 1 1. Simplify the expression. (r 6) +10r A1.1.3.1 Algebra 1 ECA Remediation Diagnostic Homework Review # Lesson. Solve the equation. 5x + 4x = 10 +6x + x A1..1 Lesson 3. Solve the equation. 1 +

### Example #1: Write an Equation Given Slope and a Point Write an equation in slope-intercept form for the line that has a slope of through (5, - 2).

Algebra II: 2-4 Writing Linear Equations Date: Forms of Equations Consider the following graph. The line passes through and. Notice that is the y-intercept of. You can use these two points to find the

### STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II 1 st Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 1 st Nine Weeks, 2016-2017 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

### Math Class: Algebra I. Summer Review Packet DUE DATE:

Name: 2014-15 Math Class: Algebra I Summer Review Packet DUE DATE: About Algebra I Algebra I teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions

### Exponents. Reteach. Write each expression in exponential form (0.4)

9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,

### Relations and Functions

Lesson 5.1 Objectives Identify the domain and range of a relation. Write a rule for a sequence of numbers. Determine if a relation is a function. Relations and Functions You can estimate the distance of

### Mark Twain Middle School Summer 2018

Mark Twain Middle School Summer 2018 Name: _ All rising Algebra or Algebra Honors students must complete this packet over the summer. Students entering Algebra or Algebra Honors must have mastered the

### Name: Block: Unit 2 Inequalities

Name: Block: Unit 2 Inequalities 2.1 Graphing and Writing Inequalities 2.2 Solving by Adding and Subtracting 2.3 Solving by Multiplying and Dividing 2.4 Solving Two Step and Multi Step Inequalities 2.5

### Georgia Common Core GPS Coordinate Algebra Supplement: Unit 2 by David Rennie. Adapted from the Georgia Department of Education Frameworks

Georgia Common Core GPS Coordinate Algebra Supplement: Unit 2 by David Rennie Adapted from the Georgia Department of Education Frameworks Georgia Common Core GPS Coordinate Algebra Supplement: Unit 2 by

### Section 2 Equations and Inequalities

Section 2 Equations and Inequalities The following Mathematics Florida Standards will be covered in this section: MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. MAFS.912.A-REI.1.1

### Algebra EOC Practice Test #1

Class: Date: Algebra EOC Practice Test #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. George is helping the manager of the local produce market expand

### 2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)

Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,

### Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities

Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,

### Elementary Algebra SAMPLE Final Examination Fall 2017

Elementary Algebra NAME: SAMPLE Final Examination Fall 2017 You will have 2 hours to complete this exam. You may use a calculator but must show all algebraic work in the space provided to receive full

### Math 2 Variable Manipulation Part 6 System of Equations

Name: Date: 1 Math 2 Variable Manipulation Part 6 System of Equations SYSTEM OF EQUATIONS INTRODUCTION A "system" of equations is a set or collection of equations that you deal with all together at once.

### Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1)

Keystone Exam Concept Review Name: Properties and Order of Operations COMMUTATIVE Property of: Addition ASSOCIATIVE Property of: Addition ( ) ( ) IDENTITY Property of Addition ZERO PRODUCT PROPERTY Let

### Warm Up. Unit #1: Basics of Algebra

1) Write an equation of the given points ( 3, 4) & (5, 6) Warm Up 2) Which of the following choices is the Associative Property 1) 4(x + 2) = 4x + 8 2) 4 + 5 = 5 + 4 3) 5 + ( 5) = 0 4) 4 + (3 + 1) = (4

### Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles

Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and

### Unit Essential Questions. How can you represent quantities, patterns, and relationships? How are properties of real numbers related to algebra?

Unit Essential Questions How can you represent quantities, patterns, and relationships? How are properties of real numbers related to algebra? Williams Math Lessons TARGET RATING 3 VARIABLES AND EXPRESSIONS

### 4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag.

ALGEBRA 1 Fall 2016 Semester Exam Review Name 1. According to the data shown below, which would be the best prediction of the average cost of a -bedroom house in Georgetown in the year 2018? Year Average

### Algebra 2 Level 2 Summer Packet

Algebra Level Summer Packet This summer packet is for students entering Algebra Level for the Fall of 01. The material contained in this packet represents Algebra 1 skills, procedures and concepts that

### Mathematics Background

For a more robust teacher experience, please visit Teacher Place at mathdashboard.com/cmp3 Patterns of Change Through their work in Variables and Patterns, your students will learn that a variable is a

### Linear Functions, Equations, and Inequalities

CHAPTER Linear Functions, Equations, and Inequalities Inventory is the list of items that businesses stock in stores and warehouses to supply customers. Businesses in the United States keep about.5 trillion

### Quarter 2 400, , , , , , ,000 50,000

Algebra 2 Quarter 2 Quadratic Functions Introduction to Polynomial Functions Hybrid Electric Vehicles Since 1999, there has been a growing trend in the sales of hybrid electric vehicles. These data show

### Module 1-A Linear Inequalities. C. x > 3 D. x < 3 A. 4.4 B. 4.5 C. 4.6 D. 4.7

Name: Date: 1. The inequality 3x + 2 > x + 8 is equivalent to. x > 3 2. x > 3 2 C. x > 3 D. x < 3 2. The inequality 2x > x + 7 is equivalent to. x > 7. x < 7 C. x = 7 D. x > 7 3 3. Which number is not

### SY14-15 Algebra Exit Exam - PRACTICE Version

Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your

### 6 which of the following equations would give you a system of equations with the same line and infinitely many solutions?

Algebra 1 4 1 Worksheet Name: Per: Part I: Solve each system of equations using the graphing method. 1) y = x 5 ) -x + y = 6 y = x + 1 y = -x 3) y = 1 x 3 4) 4x y = 8 y = 1 x + 1 y = x + 3 5) x + y = 6

### Algebra EOC Practice Test #1

Class: Date: Algebra EOC Practice Test #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. George is helping the manager of the local produce market expand

### 5 1 Worksheet MATCHING: For # 1 4, match each graph to its equation. Not all equations will be used. 1) 2) 3) 4)

Algebra 1 Name: Per: 5 1 Worksheet MATCHING: For # 1 4, match each graph to its equation. Not all equations will be used. 1) 2) 3) 4) A) yy = xx 3 B) yy = xx + 3 C) yy = 1 2 xx 3 D) yy = xx 3 E) yy = 2

### Algebra I Notes Unit Five: Linear Inequalities in One Variable and Absolute Value Equations & Inequalities

Syllabus Objective 4.4 The student will solve linear inequalities and represent the solution graphically on a number line and algebraically. Inequality Symbols: < less than less than or equal to > greater

### Unit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles

Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and

### Algebra 1 Unit 6: Linear Inequalities and Absolute Value Guided Notes

Section 6.1: Solving Inequalities by Addition and Subtraction How do we solve the equation: x 12 = 65? How do we solve the equation: x 12 < 65? Graph the solution: Example 1: 12 y 9 Example 2: q + 23

### Algebra I Summer Review Packet

Algebra I Summer Review Packet DUE THE FIRST DAY OF CLASS Name: Dear Algebra I Students and Parents, The problems in this packet are designed to help you review topics that are important to your success

### Common Core Standards Addressed in this Resource

Common Core Standards Addressed in this Resource.EE.3 - Apply the properties of operations to generate equivalent expressions. Activity page: 4 7.RP.3 - Use proportional relationships to solve multistep

Foundations of Math Chapter 3 Packet Name: Table of Contents Notes #43 Solving Systems by Graphing Pg. 1-4 Notes #44 Solving Systems by Substitution Pg. 5-6 Notes #45 Solving by Graphing & Substitution

### Week 7 Algebra 1 Assignment:

Week 7 Algebra 1 Assignment: Day 1: Chapter 3 test Day 2: pp. 132-133 #1-41 odd Day 3: pp. 138-139 #2-20 even, 22-26 Day 4: pp. 141-142 #1-21 odd, 25-30 Day 5: pp. 145-147 #1-25 odd, 33-37 Notes on Assignment:

### Complete Week 6 Package

Complete Week 6 Package HighSchoolMathTeachers@2018 Table of Contents Unit 2 Pacing Chart -------------------------------------------------------------------------------------------- 1 Day 26 Bellringer

### SOLVING LINEAR INEQUALITIES

Topic 15: Solving linear inequalities 65 SOLVING LINEAR INEQUALITIES Lesson 15.1 Inequalities on the number line 15.1 OPENER Consider the inequality x > 7. 1. List five numbers that make the inequality

### Algebra I Chapter 6 Practice Test

Name: Class: Date: ID: A Algebra I Chapter 6 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Find a solution of the system of linear inequalities.

### Unit 2 Day 3 MATRICES. MATRIX Applications Quiz 1

Unit 2 Day 3 MATRICES MATRIX Applications Quiz 1 Remember: Phones OFF Warm-Up and in Blue Pockets! Check the list. Tracey, Danica, and Sherri bought snacks for a girls sleepover. They each bought the items

### N-Q.2. Define appropriate quantities for the purpose of descriptive modeling.

Radnor High School Course Syllabus Revised 9/1/2011 Algebra 1 0416 Credits: 1.0 Grades: 9 Weighted: no Prerequisite: teacher recommendation Length: full year Format meets daily Overall Description of Course

### Algebra 1 STAAR EOC Review #7 Reporting Category 4: Linear Equations and Inequalities

Name Class Date RC3 A.07A Algebra 1 STAAR EOC Review #7 Reporting Category 4: Linear Equations and Inequalities 1. Passengers on many commercial flights may make calls from a telephone provided by the

### Graphing Linear Inequalities

Graphing Linear Inequalities Linear Inequalities in Two Variables: A linear inequality in two variables is an inequality that can be written in the general form Ax + By < C, where A, B, and C are real

### Midterm: Wednesday, January 23 rd at 8AM Midterm Review

Name: Algebra 1 CC Period: Midterm: Wednesday, January 23 rd at 8AM Midterm Review Unit 1: Building Blocks of Algebra Number Properties (Distributive, Commutative, Associative, Additive, Multiplicative)

### Chapter 4.1 Introduction to Relations

Chapter 4.1 Introduction to Relations The example at the top of page 94 describes a boy playing a computer game. In the game he has to get 3 or more shapes of the same color to be adjacent to each other.

### LESSON 2 ALGEBRA & FUNCTIONS

LESSON ALGEBRA & FUNCTIONS A) SIMPLIFYING EXPRESSIONS An expression does not have an equal sign with a left side and a right side. In an expression we can only simplify rather than solve. Simplify each

### Math 155 Prerequisite Review Handout

Math 155 Prerequisite Review Handout August 23, 2010 Contents 1 Basic Mathematical Operations 2 1.1 Examples...................................... 2 1.2 Exercises.......................................

### Algebra I EOC Review (Part 2)

1. Let x = total miles the car can travel Answer: x 22 = 18 or x 18 = 22 2. A = 1 2 ah 1 2 bh A = 1 h(a b) 2 2A = h(a b) 2A = h a b Note that when solving for a variable that appears more than once, consider

### 2(m + 3) + 5 = 7(4 m) 5m Simplify both sides of the equation using order of operations. Solution

Unit 2, Activity 2, Split-Page Notetaking Example 2(m + 3) + 5 = 7(4 m) 5m Simplify both sides of the equation using order of operations. 2m + 6 + 5 = 28 7m 5m 2m + 11 = 28 12m +12m +12m 14m + 11 = 28-11

### Algebra 2 Summer Work Packet Review and Study Guide

Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the nine specific concepts covered in the

### Honors Algebra 2 Summer Practice Problems 2017

Honors Algebra II Summer Assignment 017 These are the directions for your summer assignment for next year s course. This is an opportunity for you to review selected topics from Algebra One to make sure

### Section 1.1 Solving Linear Equations and Inequalities a + 4b c

Section 1 Solving Linear Equations and Inequalities A. Evaluating Expressions Examples Evaluate the following if a = 7, b =, and c = ( a + c ) + b. a + b c B. The Distributive Property Try the Following

### Final Exam Study Guide

Algebra 2 Alei - Desert Academy 2011-12 Name: Date: Block: Final Exam Study Guide 1. Which of the properties of real numbers is illustrated below? a + b = b + a 2. Convert 6 yards to inches. 3. How long

### Equations can be classified according to the types of operations and quantities involved. Important types include:

UNIT 5. EQUATIONS AND SYSTEM OF EQUATIONS EQUATIONS An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions

### Graph Solution Of Inequality

We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with graph solution of inequality.

### Lesson: Slope. Warm Up. Unit #2: Linear Equations. 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0)

Warm Up 1) 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0) Oct 15 10:21 AM Unit #2: Linear Equations Lesson: Slope Oct 15 10:05 AM 1 Students will be able to find the slope Oct 16 12:19

### The steps in Raya s solution to 2.5 (6.25x + 0.5) = 11 are shown. Select the correct reason for line 4 of Raya s solution.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions. Unit 2: Reasoning with Linear Equations and Inequalities The perimeter

Copyright 2015 Edmentum All rights reserved. Linear Equations & Graphs 1. A line has a y intercept of and a slope of. Find the equation of the line. A. B. C. D. Evaluate Functions 2. The graph of the function

### Algebra I Pre-AP Summer Packet

Algebra I Pre-AP Summer Packet Name: This packet is intended to give students an opportunity to recall the main concepts from 8 th Grade Math in order to facilitate their transition to Algebra I Pre-AP.

### Practice Ace Problems

Unit 5: Moving Straight Ahead Investigation 3: Solving Equations using tables and Graphs Practice Ace Problems Directions: Please complete the necessary problems to earn a maximum of 16 points according

### 4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the

### How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality

. Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and

### 1. Determine whether the given number is a solution of the equation.

Section 1.8: EXPONENTS AND ORDER OF OPERATIONS When you are done with your homework you should be able to Evaluate exponential expressions Simplify algebraic expressions with exponents Use the order of

### 28 (Late Start) 7.2a Substitution. 7.1b Graphing with technology Feb 2. 4 (Late Start) Applications/ Choosing a method

Unit 7: Systems of Linear Equations NAME: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay attention and

### Algebra I Notes Unit Five: Linear Inequalities in One Variable and Absolute Value Equations & Inequalities

Syllabus Objective 4.4 The student will solve linear inequalities and represent the solution graphically on a number line and algebraically. Inequality Symbols: < less than less than or equal to > greater

### NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve = 6 3v = -3(c + 5)

FINAL EXAM REVIEW, p. 1 NAME DATE PER. FALL FINAL EXAM REVIEW ALGEBRA 1 Solve. 1. 24 = 6 3v 2. 12 = -3(c + 5) 3. 5 2(x 3) = 63 4. 7x + 2(x - 5) = 4(x + 8) 5. r 1 10 3 2 6. x 1 2x 2 5 4 Write an equation,

### NAME DATE PER. REVIEW: FUNCTIONS PART 2

NAME DATE PER. REVIEW: FUNCTIONS PART 2 Match graphs A - G to each description. Then identify the independent & dependent variable. Description Graph (letter) x-axis (independent) y-axis (dependent) 1.

### Linear Equations and Inequalities

Unit 2 Linear Equations and Inequalities 9/26/2016 10/21/2016 Name: By the end of this unit, you will be able to Use rate of change to solve problems Find the slope of a line Model real-world data with

### Archdiocese of Washington Catholic Schools Academic Standards Mathematics

ALGEBRA 1 Standard 1 Operations with Real Numbers Students simplify and compare expressions. They use rational exponents, and simplify square roots. A1.1.1 A1.1.2 A1.1.3 A1.1.4 A1.1.5 Compare real number

### Chapter 1. ANALYZE AND SOLVE LINEAR EQUATIONS (3 weeks)

Chapter 1. ANALYZE AND SOLVE LINEAR EQUATIONS (3 weeks) Solve linear equations in one variable. 8EE7ab In this Chapter we review and complete the 7th grade study of elementary equations and their solution

### ALGEBRA MIDTERM REVIEW SHEET

Name Date Part 1 (Multiple Choice): Please show ALL work! ALGEBRA MIDTERM REVIEW SHEET 1) The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales during two class

### LINEAR EQUATIONS Modeling Linear Equations Common Core Standards

E Linear Equations, Lesson 1, Modeling Linear Functions (r. 2018) LINEAR EQUATIONS Modeling Linear Equations Common Core Standards F-BF.A.1 Write a function that describes a relationship between two quantities.

### 3.6.1 Building Functions from Context. Warm Up

Name: # Honors Coordinate Algebra: Period Ms. Pierre Date: 3.6.1 Building Functions from Context Warm Up 1. Willem buys 4 mangoes each week, and mango prices vary from week to week. Write an equation that

### Willmar Public Schools Curriculum Map

Note: Problem Solving Algebra Prep is an elective credit. It is not a math credit at the high school as its intent is to help students prepare for Algebra by providing students with the opportunity to

### ALGEBRA 1. Unit 3 Chapter 6. This book belongs to: Teacher:

ALGEBRA 1 Teacher: Unit 3 Chapter 6 This book belongs to: UPDATED FALL 2016 1 2 Algebra 1 Section 6.1 Notes: Graphing Systems of Equations Day 1 Warm-Up 1. Graph y = 3x 1 on a coordinate plane. 2. Check

### Algebra 1 End-of-Course Assessment Practice Test with Solutions

Algebra 1 End-of-Course Assessment Practice Test with Solutions For Multiple Choice Items, circle the correct response. For Fill-in Response Items, write your answer in the box provided, placing one digit