Notes 6-1. Solving Inequalities: Addition and Subtraction. y 2x 3

Size: px
Start display at page:

Download "Notes 6-1. Solving Inequalities: Addition and Subtraction. y 2x 3"

Transcription

1 Notes 6-1 Solving Inequalities: Addition and Subtraction y 2x 3

2 I. Review: Inequalities A. An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: < > A < B A > B A B A B A B A is less than B. A is greater than B. A is less than or equal to B. A is greater than or equal to B. A is not equal to B. A solution of an inequality is any value that makes the inequality true. The set of all solutions of an inequality is its solution set.

3 II. Graphing Inequalities on a Number Line A. How to Graph Inequalities Graphing Inequalities WORDS ALGEBRA GRAPH All real numbers less than 5 All real numbers greater than -1 All real numbers less than or equal to 1/2 All real numbers greater than or equal to 0 x < 5 x > -1 x 1/2 x /

4 B. Examples Graph each inequality. Ex 1: c > 2.5 Draw an empty circle at Shade in all the numbers greater than 2.5 and draw an arrow pointing to the right. Graph each inequality. 8 Ex 2:. m 3 Draw a solid circle at Shade in all numbers less than 3 and draw an arrow pointing to the left.

5 III. Writing Inequalities Write the inequality shown by each graph. Ex. 1. x < 2 Use any variable. The arrow points to the left, so use either < or. The empty circle at 2 means that 2 is not a solution, so use <. Ex. 2. x 0.5 Use any variable. The arrow points to the right, so use either > or. The solid circle at 0.5 means that 0.5 is a solution, so use.

6 IV. Set-Builder Notation You have seen that one way to show the solution set of an inequality is by using a graph. Another way is to use set-builder notation. The set of all numbers x such that x has the given property. {x : x < 6} Read the above as the set of all numbers x such that x is less than 6.

7 V. Solving Inequalities A. With a few exceptions (which we will get to tomorrow), we solve inequalities in the same way we solve equations. Pretend the inequality symbol is an equal symbol. Ex 1: Solve the inequality and graph the solutions. x + 12 < x + 0 < 8 x < Since 12 is added to x, subtract 12 from both sides to undo the addition. Draw an empty circle at 8. Shade all numbers less than 8 and draw an arrow pointing to the left.

8 B. Checking Solutions Since there can be an infinite number of solutions to an inequality, it is not possible to check all the solutions. You can check the endpoint and the direction of the inequality symbol. Ex: The solutions of x + 9 < 15 are given by x < 6.

9 Caution! In Step 1, the endpoint should be a solution of the related equation, but it may or may not be a solution of the inequality.

10 Ex 2: Solve the inequality and graph the solutions. d 5 > d + 0 > 2 d > 2 Since 5 is subtracted from d, add 5 to both sides to undo the subtraction. Draw an empty circle at Shade all numbers greater than 2 and draw an arrow pointing to the right.

11 Ex 3: Solve the inequality and graph the solutions. 0.9 n 0.3 Since 0.3 is subtracted from n, add 0.3 to both 1.2 n 0 sides to undo the 1.2 n subtraction Draw a solid circle at 1.2. Shade all numbers less than 1.2 and draw an arrow pointing to the left.

12 Ex 4: Solve each inequality and graph the solutions. a. s s s 9 Since 1 is added to s, subtract 1 from both sides to undo the addition b. > 3 + t > 0 + t t < Since 3 is added to t, add 3 to both sides to undo the addition

13 VI. Reading Math Common Phrase Equivalent Phrase Symbol No more than At most No less than At least Less than or equal to Less than or equal to Greater than or equal to Greater than or equal to

14 Ex. 1. Ray s dad told him not to turn on the air conditioner unless the temperature is at least 85 F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions. Let t represent the temperatures at which Ray can turn on the air conditioner. Turn on the AC when temperature is at least 85 F t 85 t 85 Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right

15 Ex. 2: A store s employees earn at least $8.25 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions. Let d represent the amount an employee can earn per hour. An employee earns at least $8.25 d 8.25 d

16 4. A certain restaurant has room for 120 customers. On one night, there are 72 customers dining. Write and solve an inequality to show how many more people can eat at the restaurant. x ; x 48, where x is a natural number

17 Lesson Quiz: Part I 1. Describe the solutions of 7 < x + 4. all real numbers greater than 3 2. Graph h Write the inequality shown by each graph. 3. x 3 4. x < 5.5

18 Lesson Quiz: Part II 5. A cell phone plan offers free minutes for no more than 250 minutes per month. Define a variable and write an inequality for the possible number of free minutes. Graph the solution. Let m = number of minutes. 0 m

19 Lesson Quiz: Part III Solve each inequality and graph the solutions < x + 7 x > h 15 h y 2.1 y 8.8

3-1 Graphing and Writing Inequalities. Warm Up Lesson Presentation Lesson Quiz

3-1 Graphing and Writing Inequalities. Warm Up Lesson Presentation Lesson Quiz 3-1 Graphing and Writing Inequalities Warm Up Lesson Presentation Lesson Quiz Holt Holt Algebra Algebra 1 1 Bell Quiz 3-1 Compare. Write , or =. 2 pts 1. 3 2 2 pts 2. 6.5 6.3 1 pt for putting your

More information

2-2. Warm Up Lesson Presentation Lesson Quiz

2-2. Warm Up Lesson Presentation Lesson Quiz Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Graph each inequality. Write an inequality for each situation. 1. The temperature must be at least 10 F. x 10 10 0 10 2.

More information

Chapter 3: Inequalities

Chapter 3: Inequalities Chapter 3: Inequalities 3-1: Graphing and Writing Inequalities Objectives: Identify solutions of inequalities in one variable. Write and graph inequalities in one variable. Inequality: The quantities are

More information

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

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,

More information

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

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

More information

2-4. Warm Up Lesson Presentation Lesson Quiz

2-4. Warm Up Lesson Presentation Lesson Quiz Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 2x 5 = 17 6 2. 14 Solve each inequality and graph the solutions. 3. 5 < t + 9 t > 4 4. a 8 Objective

More information

Algebra I Chapter 6: Solving and Graphing Linear Inequalities

Algebra I Chapter 6: Solving and Graphing Linear Inequalities Algebra I Chapter 6: Solving and Graphing Linear Inequalities Jun 10 9:21 AM Chapter 6 Lesson 1 Solve Inequalities Using Addition and Subtraction Vocabulary Words to Review: Inequality Solution of an Inequality

More information

2-3. Solving Inequalities by Multiplying or Dividing. Holt McDougal Algebra 1

2-3. Solving Inequalities by Multiplying or Dividing. Holt McDougal Algebra 1 Example 1A: by a Positive Number Solve the inequality and graph the solutions. 7x > 42 7x > 42 > Since x is multiplied by 7, divide both sides by 7 to undo the multiplication. 1x > 6 x > 6 10 8 6 4 2 0

More information

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

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 (>,

More information

Unit 1 Writing and Evaluating Algebraic Expressions

Unit 1 Writing and Evaluating Algebraic Expressions CC Math 1A Name Unit 1 Writing and Evaluating Algebraic Expressions Day Date Lesson Assignment Mon 8/25 Lesson 1 Writing and Evaluating Algebraic Expressions Tues 8/26 Lesson 2 Combining Like Terms & Distributive

More information

Writing and Graphing Inequalities

Writing and Graphing Inequalities 4.1 Writing and Graphing Inequalities solutions of an inequality? How can you use a number line to represent 1 ACTIVITY: Understanding Inequality Statements Work with a partner. Read the statement. Circle

More information

ACTIVITY: Areas and Perimeters of Figures

ACTIVITY: Areas and Perimeters of Figures 4.4 Solving Two-Step Inequalities the dimensions of a figure? How can you use an inequality to describe 1 ACTIVITY: Areas and Perimeters of Figures Work with a partner. Use the given condition to choose

More information

Discovering Algebra. Unit 4 Solving Inequalities & Systems of Inequalities Ch

Discovering Algebra. Unit 4 Solving Inequalities & Systems of Inequalities Ch Discovering Algebra Unit 4 Solving Inequalities & Systems of Inequalities Ch. 5.5 5.7 Unit 4: Linear Systems of Equations & Inequalities (Ch. 5) ACT Standards A 604. Solve systems of two linear equations

More information

Solving and Graphing Inequalities

Solving and Graphing Inequalities Solving and Graphing Inequalities Graphing Simple Inequalities: x > 3 When finding the solution for an equation we get one answer for x. (There is only one number that satisfies the equation.) For 3x 5

More information

Lesson 3-7: Absolute Value Equations Name:

Lesson 3-7: Absolute Value Equations Name: Lesson 3-7: Absolute Value Equations Name: In this activity, we will learn to solve absolute value equations. An absolute value equation is any equation that contains an absolute value symbol. To start,

More information

5( 4) 4 = x. Answers to Warm Up: Solve the equation and then graph your solution on the number line below.

5( 4) 4 = x. Answers to Warm Up: Solve the equation and then graph your solution on the number line below. Grade Level/Course: Grade 7, Grade 8, and Algebra 1 Lesson/Unit Plan Name: Introduction to Solving Linear Inequalities in One Variable Rationale/Lesson Abstract: This lesson is designed to introduce graphing

More information

Interactive Study Guide Solving Two-Step Equations

Interactive Study Guide Solving Two-Step Equations 11-1 To solve equations with more than one operation, or a two-step equation, follow the order of operations in reverse. First add or subtract then, multiply or divide. Solving Two-Step Equations Using

More information

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

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

More information

Unit Essential Questions. How do you represent relationships between quantities that are not equal?

Unit Essential Questions. How do you represent relationships between quantities that are not equal? Unit Essential Questions How do you represent relationships between quantities that are not equal? Can inequalities that appear to be different be equivalent? How can you solve inequalities? Williams Math

More information

Learning Log Title: CHAPTER 6: SOLVING INEQUALITIES AND EQUATIONS. Date: Lesson: Chapter 6: Solving Inequalities and Equations

Learning Log Title: CHAPTER 6: SOLVING INEQUALITIES AND EQUATIONS. Date: Lesson: Chapter 6: Solving Inequalities and Equations Chapter 6: Solving Inequalities and Equations CHAPTER 6: SOLVING INEQUALITIES AND EQUATIONS Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 6: Solving Inequalities and Equations

More information

Lesson ACTIVITY: Tree Growth

Lesson ACTIVITY: Tree Growth Lesson 3.1 - ACTIVITY: Tree Growth Obj.: use arrow diagrams to represent expressions. evaluate expressions. write expressions to model realworld situations. Algebraic expression - A symbol or combination

More information

CHAPTER 4: Polynomial and Rational Functions

CHAPTER 4: Polynomial and Rational Functions MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

More information

AdvAlg5.1InequalitiesAndCompoundSentences.notebook February 22, 2018

AdvAlg5.1InequalitiesAndCompoundSentences.notebook February 22, 2018 Nov 12 12:23 PM 1 1) When is a mathematical sentence called an inequality? A mathematical sentence which uses at least one of the following symbols: is less than is less than or equal to is greater than

More information

3) x -7 4) 3 < x. When multiplying or dividing by a NEGATIVE number, we SWITCH the inequality sign!

3) x -7 4) 3 < x. When multiplying or dividing by a NEGATIVE number, we SWITCH the inequality sign! Name: Date: / / WARM UP 1) What is the difference between an inequality and an equation.? QUIZ DAY! 2) One must be at least 35 years old in order to be president of the United States. If x represents age,

More information

CHAPTER 4: Polynomial and Rational Functions

CHAPTER 4: Polynomial and Rational Functions MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

More information

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 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

More information

Algebra II A Guided Notes

Algebra II A Guided Notes Algebra II A Guided Notes Name Chapter 1 Period Notes 1-5 Learning Matrix Goal #9: I can solve inequalities. Learning Matrix Goal #10: I can solve real-world problems involving inequalities. Learning Matrix

More information

Section 1.1: Patterns in Division

Section 1.1: Patterns in Division Section 1.1: Patterns in Division Dividing by 2 All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8. Dividing by 4 1. Are the last two digits in your number divisible by 4? 2.

More information

Up In the Air Lesson 15-1 Representing Situations with Inequalities

Up In the Air Lesson 15-1 Representing Situations with Inequalities Up In the Air Lesson 15-1 Learning Targets: Write inequalities to represent constraints or conditions within problems. Use substitution to determine whether a given number makes an inequality true. Graph

More information

SOLVING INEQUALITIES and 9.1.2

SOLVING INEQUALITIES and 9.1.2 SOLVING INEQUALITIES 9.1.1 and 9.1.2 To solve an inequality in one variable, first change it to an equation and solve. Place the solution, called a boundary point, on a number line. This point separates

More information

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

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

More information

Practice A. Inequalities. Choose an inequality for each situation. x > 10 x 10 x < 10 x 10

Practice A. Inequalities. Choose an inequality for each situation. x > 10 x 10 x < 10 x 10 Practice A Choose an inequality for each situation. x > 10 x 10 x < 10 x 10 1. The temperature today will be at least 10 F. 2. The temperature tomorrow will be no more than 10 F. 3. Yesterday, there was

More information

C. Incorrect! This symbol means greater than or equal to or at least. D. Correct! This symbol means at most or less than or equal to.

C. Incorrect! This symbol means greater than or equal to or at least. D. Correct! This symbol means at most or less than or equal to. SAT Math - Problem Drill 10: Inequalities No. 1 of 10 1. Choose the inequality symbol that means at most. (A) > (B) < (C) (D) (E) This symbol means greater than. This symbol means less than. This symbol

More information

CLASS NOTES: 2 1 thru 2 3 and 1 1 Solving Inequalities and Graphing

CLASS NOTES: 2 1 thru 2 3 and 1 1 Solving Inequalities and Graphing page 1 of 19 CLASS NOTES: 2 1 thru 2 3 and 1 1 Solving Inequalities and Graphing 1 1: Real Numbers and Their Graphs Graph each of the following sets. Positive Integers: { 1, 2, 3, 4, } Origin: { 0} Negative

More information

Writing and Graphing Inequalities

Writing and Graphing Inequalities .1 Writing and Graphing Inequalities solutions of an inequality? How can you use a number line to represent 1 ACTIVITY: Understanding Inequality Statements Work with a partner. Read the statement. Circle

More information

Egyptian Fractions: Part I

Egyptian Fractions: Part I Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker

More information

inequalities Solutions Key _ 6x 41 Holt McDougal Algebra 1 think and discuss 2-1 Check it out! b w 4-4 w

inequalities Solutions Key _ 6x 41 Holt McDougal Algebra 1 think and discuss 2-1 Check it out! b w 4-4 w CHAPTER Inequalities Solutions Key Are You Ready?. B. E. F. D. C 6. b - a = 6 - = 7. ab = ()(6) = 9. a + b = + 6 = 8 8. b a = 6 =. .. % =..

More information

Evaluate algebraic expressions and use exponents. Translate verbal phrases into expressions.

Evaluate algebraic expressions and use exponents. Translate verbal phrases into expressions. Algebra 1 Notes Section 1.1: Evaluate Expressions Section 1.3: Write Expressions Name: Hour: Objectives: Section 1.1: (The "NOW" green box) Section 1.3: Evaluate algebraic expressions and use exponents.

More information

< > less than fewer than

< > less than fewer than Name Date Algebra I Data Sheet # Writing, Solving, and Graphing Inequalities- One-step, Multistep, and Compound How do you write, solve and graph inequalities? inequality set-builder notation Key Terms

More information

Name Class Date. Properties of Inequality

Name Class Date. Properties of Inequality Name Class Date 2-2 Solving Inequalities by Adding or Subtracting Going Deeper Essential question: How can you use properties to justify solutions to inequalities that involve addition and subtraction?

More information

Math 4: Advanced Algebra Ms. Sheppard-Brick A Quiz Review Learning Targets

Math 4: Advanced Algebra Ms. Sheppard-Brick A Quiz Review Learning Targets 5A Quiz Review Learning Targets 4.4 5.5 Key Facts Graphing one-variable inequalities (ex. x < 4 ) o Perform algebra steps to get x alone! If you multiply or divide by a negative number, you must flip the

More information

Solving Two-Step Equations

Solving Two-Step Equations Solving Two-Step Equations Warm Up Problem of the Day Lesson Presentation 3 Warm Up Solve. 1. x + 12 = 35 2. 8x = 120 y 9 3. = 7 4. 34 = y + 56 x = 23 x = 15 y = 63 y = 90 Learn to solve two-step equations.

More information

Linear Functions, Equations, and Inequalities

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

More information

Section 1.4 Circles. Objective #1: Writing the Equation of a Circle in Standard Form.

Section 1.4 Circles. Objective #1: Writing the Equation of a Circle in Standard Form. 1 Section 1. Circles Objective #1: Writing the Equation of a Circle in Standard Form. We begin by giving a definition of a circle: Definition: A Circle is the set of all points that are equidistant from

More information

R.2 Number Line and Interval Notation

R.2 Number Line and Interval Notation 8 R.2 Number Line and Interval Notation As mentioned in the previous section, it is convenient to visualise the set of real numbers by identifying each number with a unique point on a number line. Order

More information

CLEP College Algebra - Problem Drill 21: Solving and Graphing Linear Inequalities

CLEP College Algebra - Problem Drill 21: Solving and Graphing Linear Inequalities CLEP College Algebra - Problem Drill 21: Solving and Graphing Linear Inequalities No. 1 of 10 1. Which inequality represents the statement three more than seven times a real number is greater than or equal

More information

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

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

More information

Egyptian Fractions: Part I

Egyptian Fractions: Part I Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker

More information

1.1 Expressions and Formulas Algebra II

1.1 Expressions and Formulas Algebra II 1.1 Expressions and Formulas Algebra II Overall Goal A1.1.1: Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and

More information

MATCHING. Match the correct vocabulary word with its definition

MATCHING. Match the correct vocabulary word with its definition Name Algebra I Block UNIT 2 STUDY GUIDE Ms. Metzger MATCHING. Match the correct vocabulary word with its definition 1. Whole Numbers 2. Integers A. A value for a variable that makes an equation true B.

More information

Functions. Content Summary

Functions. Content Summary CHAPTER 7 Functions Content Summary In Chapter 7, students increase their understanding of linear growth and equations by looking in detail at the special kind of relation called a function. This section

More information

Quadratic and Polynomial Inequalities in one variable have look like the example below.

Quadratic and Polynomial Inequalities in one variable have look like the example below. Section 8 4: Polynomial Inequalities in One Variable Quadratic and Polynomial Inequalities in one variable have look like the example below. x 2 5x 6 0 (x 2) (x + 4) > 0 x 2 (x 3) > 0 (x 2) 2 (x + 4) 0

More information

Graph Solution Of Inequality

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.

More information

Lesson 9: Introduction to Inequalities

Lesson 9: Introduction to Inequalities Opening Exercise - [adapted from MARS Evaluating Statements About Number Operations] 1. Abigail is thinking of a number. A. Could Abigail be thinking of 8? Explain your answer. B. What numbers could she

More information

Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept.

Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept. 6-1 Reteaching Graphing is useful for solving a system of equations. Graph both equations and look for a point of intersection, which is the solution of that system. If there is no point of intersection,

More information

Rev Name Date. . For example: 5x 3x

Rev Name Date. . For example: 5x 3x Name Date TI-84+ GC 7 Testing Polynomial Inequalities in One Variable Objectives: Review algebraic method for solving polynomial inequalities Review the signs of y-coordinates of points in each quadrant

More information

6th Grade. Equations & Inequalities.

6th Grade. Equations & Inequalities. 1 6th Grade Equations & Inequalities 2015 12 01 www.njctl.org 2 Table of Contents Equations and Identities Tables Determining Solutions of Equations Solving an Equation for a Variable Click on a topic

More information

USING THE QUADRATIC FORMULA and 9.1.3

USING THE QUADRATIC FORMULA and 9.1.3 Chapter 9 USING THE QUADRATIC FORMULA 9.1.2 and 9.1.3 When a quadratic equation is not factorable, another method is needed to solve for x. The Quadratic Formula can be used to calculate the roots of a

More information

Basic Equations and Inequalities. An equation is a statement that the values of two expressions are equal.

Basic Equations and Inequalities. An equation is a statement that the values of two expressions are equal. Hartfield College Algebra (Version 2018 - Thomas Hartfield) Unit ZERO Page - 1 - of 7 Topic 0: Definition: Ex. 1 Basic Equations and Inequalities An equation is a statement that the values of two expressions

More information

A constant is a value that is always the same. (This means that the value is constant / unchanging). o

A constant is a value that is always the same. (This means that the value is constant / unchanging). o Math 8 Unit 7 Algebra and Graphing Relations Solving Equations Using Models We will be using algebra tiles to help us solve equations. We will practice showing work appropriately symbolically and pictorially

More information

Chapter Two B: Linear Expressions, Equations, and Inequalities

Chapter Two B: Linear Expressions, Equations, and Inequalities Chapter Two B: Linear Expressions, Equations, and Inequalities Index: A: Intro to Inequalities (U2L8) Page 1 B: Solving Linear Inequalities (U2L9) Page 7 C: Compound Inequalities (And) (U2L10/11) Page

More information

Solving Equations by Multiplying or Dividing

Solving Equations by Multiplying or Dividing 2-2 Warm Up Lesson Presentation Lesson Quiz Bell Quiz 2-2 3 pts Solve each equation. Check your answer. 1. u -15 = -8 3 pts 3 pts 2. 19 + a = 19 3. -12 + f = 3 10 pts possible 1 pt for putting your name

More information

Linear And Exponential Algebra Lesson #1

Linear And Exponential Algebra Lesson #1 Introduction Linear And Eponential Algebra Lesson # Algebra is a very powerful tool which is used to make problem solving easier. Algebra involves using pronumerals (letters) to represent unknown values

More information

Chapter Four: Linear Expressions, Equations, and Inequalities

Chapter Four: Linear Expressions, Equations, and Inequalities Chapter Four: Linear Expressions, Equations, and Inequalities Index: A: Intro to Inequalities (U2L8) B: Solving Linear Inequalities (U2L9) C: Compound Inequalities (And) (U2L10/11) D: Compound Inequalities

More information

Chapter 5 Inequalities

Chapter 5 Inequalities Chapter 5 Inequalities 5.1 Solve inequalities using addition and subtraction 1. Write and graph an inequality. 2. Solve inequalities using addition and subtraction. Review- Symbols to KNOW < LESS THAN

More information

Standards of Learning Content Review Notes. Grade 8 Mathematics 1 st Nine Weeks,

Standards of Learning Content Review Notes. Grade 8 Mathematics 1 st Nine Weeks, Standards of Learning Content Review Notes Grade 8 Mathematics 1 st Nine Weeks, 2016-2017 Revised September 2015 2 Mathematics Content Review Notes Grade 8 Mathematics: First Nine Weeks 2015-2016 -This

More information

Pre-Algebra. Guided Notes. Unit thru 3-6, 4-3b. Equations

Pre-Algebra. Guided Notes. Unit thru 3-6, 4-3b. Equations Pre-Algebra Guided Notes Unit 4 3-1 thru 3-6, 4-3b Equations Name Lesson 3-1 Distributive Property Distributive Property used to multiply a number by a sum or difference a(b + c) = Write an equivalent

More information

2-7 Solving Absolute-Value Inequalities

2-7 Solving Absolute-Value Inequalities Warm Up Solve each inequality and graph the solution. 1. x + 7 < 4 2. 14x 28 3. 5 + 2x > 1 When an inequality contains an absolute-value expression, it can be written as a compound inequality. The inequality

More information

Solving Systems of Linear Inequalities Focus on Modeling

Solving Systems of Linear Inequalities Focus on Modeling Name Class 5-6 Date Solving Systems of Linear Inequalities Focus on Modeling Essential question: How can you use systems of linear equations or inequalities to model and solve contextual problems? N-Q.1.1*,

More information

Variables and Expressions

Variables and Expressions Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic

More information

Day 1: Introduction to Vectors + Vector Arithmetic

Day 1: Introduction to Vectors + Vector Arithmetic Day 1: Introduction to Vectors + Vector Arithmetic A is a quantity that has magnitude but no direction. You can have signed scalar quantities as well. A is a quantity that has both magnitude and direction.

More information

Lesson #9 Simplifying Rational Expressions

Lesson #9 Simplifying Rational Expressions Lesson #9 Simplifying Rational Epressions A.A.6 Perform arithmetic operations with rational epressions and rename to lowest terms Factor the following epressions: A. 7 4 B. y C. y 49y Simplify: 5 5 = 4

More information

6.5 Systems of Inequalities

6.5 Systems of Inequalities 6.5 Systems of 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 numbers

More information

Math 8 Notes Units 1B: One-Step Equations and Inequalities

Math 8 Notes Units 1B: One-Step Equations and Inequalities Math 8 Notes Units 1B: One-Step Equations and Inequalities Solving Equations Syllabus Objective: (1.10) The student will use order of operations to solve equations in the real number system. Equation a

More information

Lesson 3-6: Compound Inequalities Name:

Lesson 3-6: Compound Inequalities Name: Lesson 3-6: Compound Inequalities Name: W hen people plan a house, they often have many requirements in mind that can be written as inequalities. Such requirements could be the dimensions of rooms or the

More information

x y x y 15 y is directly proportional to x. a Draw the graph of y against x.

x y x y 15 y is directly proportional to x. a Draw the graph of y against x. 3 8.1 Direct proportion 1 x 2 3 5 10 12 y 6 9 15 30 36 B a Draw the graph of y against x. y 40 30 20 10 0 0 5 10 15 20 x b Write down a rule for y in terms of x.... c Explain why y is directly proportional

More information

Minnesota K-12 Academic Standards in Mathematics (2007)

Minnesota K-12 Academic Standards in Mathematics (2007) 8.1.1.1 Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number an irrational

More information

c) The phrase maximum refers to the inequality sign. The maximum temperature in a region of Northern Alberta is 13: x 13.

c) The phrase maximum refers to the inequality sign. The maximum temperature in a region of Northern Alberta is 13: x 13. Chapter 9 Linear Inequalities Section 9.1 Section 9.1 Page 13 Question 5 a) The phrase at least corresponds to the inequality sign. If Brent scored at least 3 points in each basketball game this season

More information

North Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents.

North Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents. North Seattle Community College Math 084 Chapter 1 Review For the test, be sure to show all work! Turn off cell phones. Perform the operation. Perform the operation. Write the product using exponents.

More information

C. Graph the solution to possibilities for Sharmara s number and give the solution in interval notation.

C. Graph the solution to possibilities for Sharmara s number and give the solution in interval notation. Homework Problem Set Sample Solutions S.77 Homework Problem Set 1. Shamara is thinking of a number. A. Could Shamara be thinking of 8? Explain. No, if Shamara thought of 8, the answer would equal 2. B.

More information

6-6 Solving Systems of Linear Inequalities 6-6. Solving Systems of Linear Inequalities

6-6 Solving Systems of Linear Inequalities 6-6. Solving Systems of Linear Inequalities 6-6 Solving Systems of Linear Inequalities Warm Up Lesson Presentation Lesson Quiz 1 2 pts 3 pts 5 pts Bell Quiz 6-6 Solve each inequality for y. 1. 8x + y < 6 2. 3x 2y > 10 3. Graph the solutions of 4x

More information

Name: Class: Date: Mini-Unit. Data & Statistics. Investigation 1: Variability & Associations in Numerical Data. Practice Problems

Name: Class: Date: Mini-Unit. Data & Statistics. Investigation 1: Variability & Associations in Numerical Data. Practice Problems Mini-Unit Data & Statistics Investigation 1: Variability & Associations in Numerical Data Practice Problems Directions: Please complete the necessary problems to earn a maximum of 5 points according to

More information

Supplementary Trig Material

Supplementary Trig Material Supplementary Trig Material Math U See Table of Contents Lesson A: Solving Equations with Radicals and Absolute Value Lesson Practice Worksheet A - 1 Lesson Practice Worksheet A - 2 Lesson B: Solving Inequalities

More information

7 = 8 (Type a simplified fraction.)

7 = 8 (Type a simplified fraction.) Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation. 3. 10 6 10. 3. 4. 3. 10 6 10 = (Use the multiplication symbol

More information

b. Why do you suppose the percentage of women doctors has been increasing over the past 40 years?

b. Why do you suppose the percentage of women doctors has been increasing over the past 40 years? Special Topics: U3. L2. Inv 1 Name: Homework: Math XL Unit 3: HW: 9/14-9/18 Week 2(Due Friday, 9/18, by 11:59 pm) Lesson Target: Being able to formulate linear equations and inequalities and solutions

More information

L.4 Linear Inequalities and Interval Notation

L.4 Linear Inequalities and Interval Notation L. Linear Inequalities and Interval Notation 1 Mathematical inequalities are often used in everyday life situations. We observe speed limits on highways, minimum payments on credit card bills, maximum

More information

Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2

Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2 4-5 Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Solve. 1. log 16 x = 3 2 64 2. log x 1.331 = 3 1.1 3. log10,000 = x 4 Objectives Solve exponential and logarithmic equations and equalities.

More information

2-2. Learn to translate between words and math. Course 1

2-2. Learn to translate between words and math. Course 1 Learn to translate between words and math. In word problems, you may need to translate words to math. Action Put together or combine Operation Add Find how much more or less Subtract Put together groups

More information

Reteaching Using Deductive and Inductive Reasoning

Reteaching Using Deductive and Inductive Reasoning Name Date Class Reteaching Using Deductive and Inductive Reasoning INV There are two types of basic reasoning in mathematics: deductive reasoning and inductive reasoning. Deductive reasoning bases a conclusion

More information

Test 3 Version A. On my honor, I have neither given nor received inappropriate or unauthorized information at any time before or during this test.

Test 3 Version A. On my honor, I have neither given nor received inappropriate or unauthorized information at any time before or during this test. Student s Printed Name: Instructor: CUID: Section: Instructions: You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes, cell phone, laptop,

More information

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

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

More information

Algebra 3-4 Unit 1 Absolute Value Functions and Equations

Algebra 3-4 Unit 1 Absolute Value Functions and Equations Name Period Algebra 3-4 Unit 1 Absolute Value Functions and Equations 1.1 I can write domain and range in interval notation when given a graph or an equation. 1.1 I can write a function given a real world

More information

Circles & Interval & Set Notation.notebook. November 16, 2009 CIRCLES. OBJECTIVE Graph a Circle given the equation in standard form.

Circles & Interval & Set Notation.notebook. November 16, 2009 CIRCLES. OBJECTIVE Graph a Circle given the equation in standard form. OBJECTIVE Graph a Circle given the equation in standard form. Write the equation of a circle in standard form given a graph or two points (one being the center). Students will be able to write the domain

More information

6-4 Solving Special Systems

6-4 Solving Special Systems 6-4 Solving Special Systems Warm Up Lesson Presentation Lesson Quiz 1 2 pts Bell Quiz 6-4 Solve the equation. 1. 2(x + 1) = 2x + 2 3 pts Solve by using any method. 2. y = 3x + 2 2x + y = 7 5 pts possible

More information

Graphing Linear Inequalities

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

More information

PENDING FINAL EDITORIAL REVIEW

PENDING FINAL EDITORIAL REVIEW Exercise 1 (5 minutes) Discuss the two-variable equation in Exercise 1 and the possible solutions represented as ordered pairs. Have students work independently, using their prior knowledge to verify which

More information

Math 1 Summer Assignment 2017

Math 1 Summer Assignment 2017 Math 1 Summer Assignment 2017 Assignment Due: Monday, August 28, 2017 Name: The following packet contains topics and definitions that you will be required to know in order to succeed in Math 1 this year.

More information

35 38 Absolute Value Quiz and Unit 8 Review.notebook April 18, Learning Target 2ab: I can write and solve absolute value equations.

35 38 Absolute Value Quiz and Unit 8 Review.notebook April 18, Learning Target 2ab: I can write and solve absolute value equations. Unit 8 Quiz #3 Absolute Value Name: Hour: Learning Target 2ab: I can write and solve absolute value equations. Solve each absolute value equation. x + 5 = 3 3 x + 5 = 6 Learning Target 3abc: I can write,

More information

Lesson 9.1 Skills Practice

Lesson 9.1 Skills Practice Lesson 9.1 Skills Practice Name Date Call to Order Inequalities Vocabulary Write the term that best completes each statement. 1. A(n) graph of an inequality in one variable is the set of all points on

More information

MATH 60 Course Notebook Chapter #1

MATH 60 Course Notebook Chapter #1 MATH 60 Course Notebook Chapter #1 Integers and Real Numbers Before we start the journey into Algebra, we need to understand more about the numbers and number concepts, which form the foundation of Algebra.

More information