1 Integrated Math 1 - Chapter 5 Homework Scoring Guide
2 Integrated Math 1 - Chapter 5 Homework Scoring Guide Lesson Lesson Title Homework Problems Score How does the pattern grow? 5-6 to How high will it bounce? 5-22 to What is the pattern? 5-35 to How can I describe a sequence? How do arithmetic sequences work? How else can I write the equation? 5-46 to to to What is the rate of change? 5-86 to How can I use a multiplier? to Is it a function? to Total Points (add all points together) Total Number of Assignments (# divided by) Average Score per Assignment
3 5-6. What if the data for Lennie and George (from problem 5-1) matched the data in each table below? Assuming that the growth of the rabbits multiplies as it did in problem 5-1, complete each of the following tables. Show your thinking or give a brief explanation of how you know what the missing entries are. a. b The equation of a line describes the relationship between the x- and y-coordinates of the points on the line. a. Plot the points (3, 1), (3, 2), and (3, 4) and draw the line that passes through them. State the coordinates of two more points on the line. Then answer this question: What will be true of the coordinates of any other point on this line? Now write an equation that says exactly the same thing. (Do not worry if it is very simple! If it accurately describes all the points on this line, it is correct.)
4 b. Plot the points (5, 1), (1, 1), and ( 3, 1). What is the equation of the line that goes through these points? Write each expression below in a simpler form. a b c. ( )0 d. ( ) Write the equation of each line described below. A line with a slope of 2 and y-intercept (0, 7). A line with a slope of 3 and x-intercept (4, 0). 2 A line perpendicular to the line in part (b) with x-intercept (4, 0).
5 5-22. Solve each equation. a. 2(x 2) = 6 b. 2(x + 1) + 3 = 3(x 1) Calculate the slope of the line through the points (6, 8) and (3, 4). Write the equation of the line. Is the point ( 3, 4) on the line you found in part (a)? How can you tell? AAA Packages Plus sends packages overnight for $5 plus $0.25 per ounce. United Packages charges $2 plus $0.35 per ounce. Mr. Molinari noticed that his package would cost the same to mail using either service. Write an equation to represent this situation. How much does Mr. Molinari s package weigh? Ms. Cai s class is studying a tile pattern. The equation for the tile pattern is y = 10x 8. Kalil thinks that Figure 12 of this pattern will have 108 tiles. Is he correct? Justify your answer.
6 5-35. DeShawna and her team gathered data for their ball and recorded it in the table shown at right. What is the rebound ratio for their ball? Predict how high DeShawna s ball will rebound if it is dropped from 275 cm. Look at the precision of DeShawna s measurements in the table. Round your calculation to a reasonable number of decimal places. Suppose the ball is dropped and you notice that its rebound height is 60 cm. From what height was the ball dropped? Use an appropriate precision for your answer. Suppose the ball is dropped from a window 200 meters up the Empire State Building. What would you predict the rebound height to be after the first bounce? How high would the ball in part (d) rebound after the second bounce? After the third bounce?
7 5-37. Write an equation for the line containing the points listed in the table. x y Solve each equation. a. 2x 8 10 = 6 b. 9 x = 3 40
8 5-46. Chelsea dropped a bouncy ball off the roof while Nery recorded its rebound height. The table at right shows their data. To what family does the function belong? Explain how you know. Write the data as a sequence. Is the sequence arithmetic, geometric, or something else? Justify your answer The average distance from the earth to the moon is meters. If the length of the average pencil is meters, approximately how many pencils would need to be connected together to reach the moon? Use appropriate precision in your answer For the line passing through the points ( 2, 1) and (2, 11): a. Calculate the slope of the line. b. Write the equation of the line.
9 5-49. Allie is making 8 dozen chocolate-chip muffins for the food fair at school. The recipe she is using makes 3 dozen muffins. If the original recipe calls for 16 ounces of chocolate chips, how many ounces of chocolate chips does she need to make 8 dozen muffins? (Allie buys her chocolate chips in bulk and can measure them to the nearest ounce.) A tank contains 8000 liters of water. Each day, half of the water in the tank is removed. How much water will be in the tank at the end of: The 4 th day? The 8 th day? Simplify each expression below. y y z 0.2z x x
10 5-53. Draw a slope triangle and use it to write the equation of the line shown in the graph below Harry the Hungry Hippo is munching on the lily pads in his pond. When he arrived at the pond, there were 20 lily pads, but he is eating 4 lily pads an hour. Heinrick the Hungrier Hippo found a better pond with 29 lily pads! He eats 7 lily pads every hour. If Harry and Heinrick start eating at the same time, when will their ponds have the same number of lily pads remaining? How many lily pads will be left in each pond at that time?
11 5-66. Determine whether 447 is a term of each sequence below. If so, which term is it? t(n) = 5n 3 d. t(n) = 14 3n t(n) = 24 5n e. t(n) = 8 7(n 1) c. t(n) = 6 + 3(n 1) Choose one of the sequences in problem 5-66 for which you determined that 447 is not a term. Write a clear explanation describing how you can be sure that 447 is not a term of the sequence.
12 5-68. Determine the common difference (sequence generator) for each arithmetic sequence listed below. Then write an equation for the n th term in each sequence, keeping in mind that the first term of each sequence is t(1). 4, 7, 10, 13, 3, 8, 13, 24, 19, 14, 7, 9.5, 12, Great Amusements Park has been raising its ticket prices every year, as shown in the table below. Describe how the ticket prices are growing. What will the price of admission be in year 6?
13 5-71. Monique and her dad built a hang glider together. After testing the new glider for safety, the glider was ready for the first big flight. Monique jumped off a tall sand dune and traveled in a diagonal line from the top of the dune toward the ground. She flew for 137 feet and landed on level ground at a spot 105 feet horizontally from where she took off. How tall was the sand dune?
14 5-77. Avery and Collin were trying to challenge each other with equations for sequences. Avery was looking at an explicit equation that Collin wrote. a. Write the first 4 terms for the sequence. t(n) = 4.5n 8 b. What would Avery do to write the 15 th term of this sequence? c. Write a recursive equation for this sequence Write both an explicit equation and a recursive equation for the sequence: 5, 8, 11, 14, 17, Compute the following products using area models. (4x + 5)(4x 5) (4x + 5) 2
15 5-80. Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has 120 stamps. Lona joined a stamp club, which sends her 12 new stamps each month. The stamp book holds a maximum of 500 stamps. Complete the table at right. How many stamps will Lona have in one year from now? Write an equation using function notation to represent the total number of stamps that Lona has in her collection after n months. Let the total be represented by t(n). Solve your equation from part (c) for n when t(n) = 500. Will Lona be able to fill her book exactly with no stamps remaining? How do you know? When will the book be filled? A calculator manufacturer offers two different models for students. The company has sold 10,000 scientific calculators so far and continues to sell 1500 per month. It has also sold 18,000 graphing calculators and continues to sell 1300 of this model each month. If at some month, m, the number of scientific calculators sold is equal to the number of graphical calculators sold, then write an equation that represents this situation. When will the number of scientific calculators sold equal the number of graphical calculators sold? That is, solve your equation from part (b) for m.
16 5-86. Identify the following sequences as arithmetic, geometric, or neither. For the arithmetic and geometric sequences, identify the growth pattern. a. 12, 144, 1728, b. 0, 5, 10, 15, 20, 25, c. 0, 4, 16, 36, 64, d. 1.5, 2.25, 3.375, , Write the first five terms of of each recursively-defined sequence. t(1) = 3 t(n + 1) = 2 t(n) t(1) = 8 t(n + 1) = t(n) 5 t(1) = 2 t(n + 1) = (t(n)) 1
17 5-88. Use angle relationships and the diagram below to write and solve an equation for x. Show all work The area of the trapezoid at right is 56 cm 2. What is the height, h? (Hint: The formula for the area of a trapezoid can be written as A = 1 (b1 + b2)h, were b1 and b2 are the lengths of the bases.) Show all 2 work Simplify each expression. (2m 3 )(4m 2 ) 6y 5 3y 2 4y 2 6y 7 ( 2x 2 ) 3
18 Convert each percent increase or decrease into a multiplier. a. 3% increase b. 25% decrease c. 13% decrease d. 2.08% increase Write the equation of the line parallel to y = 1 x + 5 passing through the point (9, 1) Solve each equation. a. 8 (2x + 1) = 3 b. x + 4 = 9
19 Zeke ran 4 miles in 45 minutes. If he keeps running at the same pace, how long will it take him to run 10 miles? What is his unit rate in miles per hour? Solve each equation. a. (x + 2)(x + 3) = x 2 10 b. 1 2 x +1 3 x 7 = 5 6 x c. x+1 3 = x 2 d. 9 x = ( 1 3 )x+3
20 What is the equation of the line that has a y-intercept of (0, 3) and passes through the point ( 9, 9)? If f(x) = 1, calculate each of the following values. x+2 f( 3) f( 1.5) f( 2) x if f(x) = 5
21 Describe the domain of each function or sequence below. a. The function f(x) = 3x 5. b. The sequence t(n) = 3n 5 c. The function f(x) = 5 x. d. The sequence t(x) = 5 n Think about the difference between a function and a sequence as you answer the questions below. A certain sequence has an explicit equation of t(n) = 5 2 n. Is it possible for this sequence to have a term with the value of 200? If so, which term is it? If not, justify why not. Now think about a function with the equation of f(x) = 5 2 x. Is it possible for this function to have an output of 200? If so, what input gives this output? If not, justify why not.
22 Read the Math Notes box in this lesson for information about an alternative notation for sequences, then use the given sequence to complete the parts below. a1 = 5 an = an Therefore: Now continue the sequence: a4 = a? +? =? a5 = a? +? =? The first 5 terms of the sequence are: The Coopersville Mad Hens baseball team played Q games last year, each consisting of 9 innings. Their star pitcher, Kasmir, pitched T innings total, walked Wbatters, and struck out K batters. The opposing batters got on base by a hit or an error H times in those innings. He made a total of P pitches for the year. What do the following expressions represent in this context? W + K + H K T 9Q T 9Q P T
23 Geoffrey and Ricardo are running a relay race. Two minutes into the race, they have run 775 meters total. If Geoffrey ran x meters of the race, write an expression that represents the distance Ricardo has run Figure 2 of a tile pattern is shown at right. If the pattern grows linearly and if Figure 5 has 15 tiles, then write an equation for the pattern.
Algebra 2 Appendix A A-6. What if the data for Lenny and George (from problem A-1) matched the data in each table below? Assuming that the growth of the rabbits multiplies as it did in problem A-1, complete
Name: Practice Integrated II Final Exam Review The questions below represent the types of questions you will see on your final exam. Your final will be all multiple choice however, so if you are able to
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
Chapter 1 Homework Problems Lesson 1.1.1 1-4. Angelica is working with function machines. She has the two machines shown at right. She wants to put them in order so that the output of the first machine
Student: Date: Instructor: TODD CONKLIN Course: 3rd hour Math Assignment: Samples and Populations Practice/ End of Year Review 1. You ask 8 classmates how many pencils they have in their bags. The mean
Applications 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars. 2 t = 0.5 + 2a, where a represents the area of the grass and t represents the time in hours
Name Date Class 7.EE.1 SELECTED RESPONSE Select the correct answer. 1. What property allows the expression.7x + 10. + 15.3x 8.x + 15.6 to be simplified to the equivalent expression 0x + 10. 8.x + 15.6?
Name Hour Algebra - Chapter 5 Review 1. Write an equation in slope-intercept form of the graph. 10 y 10 x 10 2. The cost of a school banquet is $95 plus $15 for each person attending. Write an equation
Midterm Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether or not the arrow diagram defines a function. 1) Domain Range 1) Determine
IM1 Summative Practice #1 Name: Show all your Work Period: Simplify each expression below. 1. 5x (7 3x) 2. 5(x 12) + 15(x + y) 3. 8 2(x 2 3x) (9 3x 2 ) Solve each equation. Justify each step with a property
Name: Date: Unit Multiple Choice Test Questions MCC9.F.IF. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one
Lesson 8: Representing Proportional Relationships with Equations Student Outcomes Students use the constant of proportionality to represent proportional relationships by equations in real world contexts
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
Lesson 8-4 Lesson 8-4 Radical Notation for nth Roots Vocabulary radical sign, O n x when x 0 geometric mean BIG IDEA For any integer n, the largest real nth root of x can be represented either by x 1 n
Pre-EOC Assessment Algebra1 #1 Wahkiakum School District ALG1 Page 1 A1.1.A (#1 from OSPI sample test) Text Section 1-1 1. Mrs. Morris gave her students this pattern of white tiles: She asked her students
GUIDED NOTES 4.1 LINEAR FUNCTIONS LEARNING OBJECTIVES In this section, you will: Represent a linear function. Determine whether a linear function is increasing, decreasing, or constant. Interpret slope
UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES This unit investigates linear equations and inequalities. Students create linear equations and inequalities and use them to solve problems. They
A Story of Eureka Math Grade, Module 4 Student File_B Contains Sprint and Fluency,, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may
Lesson 1-1 Use the table for Items 1 and. Canoe Rental Days Cost ($) 1 5 3 78 5 1 7 13 1. Use function notation to write a linear function that gives the cost C in dollars of renting a canoe for t days.
Page 1 ALGEBRA I END-OF-COURSE EXAM: PRACTICE TEST 1. Order the following numbers from least to greatest:, 6, 8.7 10 0, 19 b. 19,, 8.7 100, 6 6, 8.7 10 0,, 19 c. d. 8.7 10 0,, 19, 6, 6, 19, 8.7 100. If
Elementary Algebra NAME: SAMPLE Final Examination Spring 2015 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
Midterm Review Fall 018 Topics List: Unit 1 Simplifying Expressions Evaluating Linear Equations Dimensional Analysis Consecutive Number Equations Linear Equation Word Problems Representing Linear Equations
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
6 th Grade to 7 th Grade Summer Math Packet For this Math packet please show as much work as you can. The concepts you are going to be working on are those of the Common Core Standards for 6 th Grade that
Class: Date: Coordinate Algebra A Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. Do NOT write on the test. You may use your calculator.
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,
Math 060/Final Exam Review Guide/ 010-011/ College of the Canyons General Information: The final exam is a -hour timed exam. There will be approximately 40 questions. There will be no calculators or notes
Question 1. Hank bought 3 more boxes of cereal than gallons of milk. He bought x boxes of cereal at $2.79 each. Each gallon of milk costs $4.49. Consider the expression 2.79x + 4.49 (x 3). Determine if
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
Strategic Math General Review of Algebra I With Answers By: Shirly Boots 1/6 Add/Subtract/Multiply/Divide Addmoves to the right -3-2 -1 0 1 2 3 Subtract moves to the left Ex: -2 + 8 = 6 Ex: -2 8 = - 10
2-1 Practice A Solving Equations by Adding or Subtracting Solve each equation by using addition. Check your answers. 1. m 2 = 5 2. t 9 = 14 3. p 6 = 2 4. a 4.5 = 3.5 5. 3 = c 8 6. y 1 5 = 2 5 Solve each
Linear Modeling/Regression FUNCTION NOTATION Given the function notation of a coordinate: a) Rewrite the coordinate as (x, y) b) Plot the point on the graph and give the quadrant it lies in 1) f() = 2)
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
Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Ramal goes to the grocery store and buys pounds of apples and pounds of bananas. Apples cost dollars per
Algebra 1 Third Quarter Study Guide 1. Evaluate:. 2. Evaluate: 8 5 5 t. 2 s t when s = 5 and 7 Simplify. 3. 2 0 5 3 2x y x y 4. 4 3 54xy 5. 4 24 6. 3x 2 y 3 7. Is 3 a solution of? 8. A store that sells
Class: Date: Algebra, Spring Semester Review 1. (1 point) Graph the relation and its inverse. Use open circles to graph the points of the inverse. x 0 4 9 10 y 3 7 1 a. c. b. d. 1 . (1 point) Is relation
Technology Math Skills Assessment Practice Test . Which of the following is the best description of 3 5 x? a. Monomial b. Binomial c. Polynomial d. Both a and c. Create a table of values for the equation
9//7, 0) AM Lesson Problem Which one of these shapes is not like the others? Explain what makes it different by representing each width and height pair with a ratio. C is different from A and B. For both
7.4 Lesson Lesson Tutorials An equation in two variables represents two quantities that change in relationship to one another. A solution of an equation in two variables is an ordered pair that makes the
Item Specification Sheet Algebra I Semester Exam Free Response: 1. Illustrating Mathematical Properties 2. Equations with Infinitely Many Solutions or No Solution 3. Relations and Functions 4. Application
Regents Exam Questions - PH Algebra Chapter Page 1 CHAPTER -1 SLOPE AND DIRECT VARIATION 4. 069918a, P.I. 8.G.1 What is the slope of line shown in the accompanying diagram? 1. 080417a, P.I. A.A. If the
MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the
MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set
Name: Period: ate: lgebra 1 1st Semester Review 2011 1 Which algebraic expression could NOT match the pictorial representation below? 5 Which best describes the solution(s) for this equation? 3 ( 8x 12)
School District of Palm Beach County Summer Packet Algebra EOC Review Summer 2014 Students and Parents, This Summer Packet for Algebra 1 EOC Review is designed to provide an opportunity to review and remediate
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
Name: Date: Part 1 Multiple Choice Keystone Exam Practice Test # 1) Evan always drives between 45 and 60 miles per hour on his commute. The distance he travels can be represented in the system of inequalities
LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:
Math 50, Fall 2011 Test 3 PRINT your name on the back of the test. Directions 1. Time limit: 1 hour 50 minutes. 2. To receive credit on any problem, you must show work that explains how you obtained your
Dear Student: Congratulations on being placed in the GSE Accelerated Analytic Geometry B/Advanced Algebra class for the 0-09 school year! This is a fast-paced and rigorous college-preparatory math course
Algebra 1a Final Exam 2016-2017 Review Short Answer Graph the inequality. 1. x < 1 2. Solve the inequality. Then graph your solution. 3. 4. 5. 5 8 v < 7 5 6. 7. 8. 10 < 3x 7 < 17 9. Solve the inequality.
. Circle the letter that correctly lists the factors for the number given? these are multiples (more than or = to the number) a) 4: 4, 8,, 6, 0, b) 8:,, 4, 7, 4, 8 c) 4:,, 4, 6, 8,, 4 d) 6: 6,, 8, 4, 0,
PRACTICE FINAL - 1010-004, FALL 2013 If you are completing this practice final for bonus points, please use separate sheets of paper to do your work and circle your answers. Turn in all work you did to
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
Name: Features of Functions 5.1H Ready, Set, Go! Ready Topic: Solve systems by graphing For each system of linear equations: a. Graph the system b. Find the x- and y-intercepts for each equation c. Find
Skills Practice Skills Practice for Lesson. Name Date Widgets, Dumbbells, and Dumpsters Multiple Representations of Linear Functions Vocabular Write the term that best completes each statement.. A(n) is
Spring 2011 Name Math 115 Elementary Algebra Review Wednesday, June 1, 2011 All problems must me done on 8.5" x 11" lined paper. Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x
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
Name: Pd: 2016-2017 Algebra 1 PAP Fall Exam Review 1. A collection of nickels and quarters has a value of $7.30. The value of the quarters is $0.80 less than triple the value of the nickels. Which system
Correlation of From Patterns to Algebra to the Ontario Mathematics Curriculum (Grade 4) Strand: Patterning and Algebra Ontario Curriculum Outcomes By the end of Grade 4, students will: describe, extend,
Class: Date: Algebra, Spring Semester Review 01 1. (1 point) Find the annual percent increase or decrease that y = 0.5(.) x models. 0% increase 0% decrease 10% increase d. 5% decrease. (1 point) An initial
Math 1 Lesson 4-5: Completing the Square Targets: I can identify and complete perfect square trinomials. I can solve quadratic equations by Completing the Square. When a=1 in a perfect square trinomial,
Gearing Up for Geometry! Geometry is right around the corner and you need to make sure you are ready! Many of the concepts you learned in Algebra I will be used in Geometry and you will be epected to remember
7.1 The student will a) investigate and describe the concept of negative exponents for powers of ten; b) determine scientific notation for numbers greater than zero; c) compare and order fractions, decimals,
Linear Functions Rate of Change and slope Objective: To find rates of change from tables. To find slope. Objectives I can find the rate of change using a table. I can find the slope of an equation using
Name Class Date 9.3 Using the Quadratic Formula to Solve Equations Essential Question: What is the quadratic formula, and how can you use it to solve quadratic equations? Resource Locker Explore Deriving
Class: Date: Unit 3 Practice Test Describe a pattern in each sequence. What are the next two terms of each sequence? 1. 24, 22, 20, 18,... Tell whether the sequence is arithmetic. If it is, what is the
A C E Applications Connections Extensions Applications 1. Below are some results from the bridge experiment in a CMP class. Bridge-Thickness Experiment Number of Layers 2 4 6 8 Breaking Weight (pennies)
Graduation-Required Assessment for Diploma Mathematics Test Book 18pt Item Sampler Student responses in this test book must be entered by a scribe into an accommodated test form in the Data Entry Interface.
1 Integrated Math 1 Honors Module 9H Quadratic Functions Ready, Set, Go Homework Solutions Adapted from The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet
Jessie s us Ride (minutes) Jessie s us Ride (minutes) 1 Jessie s bus ride to school is 5 minutes more than 2 the time of Robert s bus ride. 3 Which graph shows the possible times of Jessie s and Robert
Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Summer 2013 Solving Linear Equations Student Packet Day 3 Name: Date: Benchmark MA.912.A.3.1 Solve linear equations in one variable that include simplifying