2-4 Solving Equations with the Variable on Each Side. Solve each equation. Check your solution x + 2 = 4x + 38 ANSWER: 4 ANSWER:

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1 1. 13x + 2 = x MULTIPLE CHOICE Find the value of x so that t figures have the same perimeter (n + ) = = (b + 5) (n + 1) = 2n r = r (2 + r) 7. 1v + 6 = 2(5 + 7v) 8. 5h 7 = 5(h 2) + 3 A B 5 C 6 D 7 A 10. 7c + 12 = c m 13 = 8m x = 2x t = 8t esolutions Manual - Powered by Cognero Page 1

2 16. 8 = (r + ) 17. 6(n + 5) = (g + 8) 7 = (3m 2) = 2(3m + 3) 21. 6(3a + 1) 30 = 3(2a ) GEOMETRY Find the value of x so the rectangles have the same area. 2. CCSS SENSE-MAKING Two times the least of three consecutive odd integers exceeds three times the greatest by 15. What are the integers? 7, 5, x = 2(x 3) (3 q) + = 5q NUMBER THEORY Four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers., esolutions Manual - Powered by Cognero Page 2

3 j 5.2 =.33j MOBILE PHONES The table shows the number of mobile phone subscribers for two states for a recent year. How long will it take for the numbers of subscribers to be the same? t 25.2 = 3.8t k.3 = 12.6k [2p (p + 5)] = NUMBER THEORY Three times the lesser of two consecutive even integers is 6 less than six times the greater number. Find the integers., years or 2 years months 1. MULTIPLE REPRESENTATIONS In this problem, you will explore 2x + = x 2. a. GRAPHICAL Make a table of values with five points for y = 2x + and y = x 2. Graph the points from the tables. b. ALGEBRAIC Solve 2x + = x 2. c. VERBAL Explain how the solution you found in part b is related to the intersection point of the graphs in part a. a. 38. MONEY Chris has saved twice the number of quarters that Nora saved plus 6. The number of quarters Chris saved is also five times the difference of the number of quarters and 3 that Nora has saved. Write and solve an equation to find the number of quarters they each have saved. 2q +6 = 5(q 3); Nora saved 7 quarters, and Chris saved 20 quarters 39. DVD A company that replicates DVDs spends $1500 per day in building overhead plus $0.80 per DVD in supplies and labor. If the DVDs sell for $1.59 per disk, how many DVDs must the company sell each day before it makes a profit? 1899 DVDs/day b. c. Sample answer: The solution in part b is the x- coordinate for the point of intersection on the graph. esolutions Manual - Powered by Cognero Page 3

4 2. REASONING Solve 5x + 2 = ax 1 for x. Assume that a 0. Describe each step. 5. CCSS CRITIQUE Determine whether each solution is correct. If the solution is not correct, describe the error and give the correct solution. a. 3. CHALLENGE Write an equation with the variable on each side of the equals sign, at least one fractional coefficient, and a solution of 6. Discuss the steps you used. Sample answer: 2x + 1 = x 2 b. c. First, I chose as the fractional coefficient. Then, I chose 2 for the coefficient for the variable on the other side of the equation. After substituting 6 in for x on both sides, 1 must be added to the left and 2 must be subtracted from the right to balance the equation.. OPEN ENDED Create an equation with at least two grouping symbols for which there is. Sample answer: 2(3x + 6) = 3(2x + 5) a. Incorrect; the 2 must be distributed over both g and 5; 6 b. Correct c. Incorrect; to eliminate 6z on the left side of the equals sign, 6z must be added to each side of the equation; CHALLENGE Find the value of k for which each equation is an identity. a. k(3x 2) = 6x b. 15y 10 + k = 2(ky 1) y a. b WRITING IN MATH Compare and contrast solving equations with variables on both sides of the equation to solving one-step or multi-step equations with a variable on one side of the equation. Sample answer: If the equation has variables on both sides of the equation, you must first add or subtract one of the terms from both sides of the equation so that the variable is left on only one side of the equation. Then, solving the equations uses the same steps. esolutions Manual - Powered by Cognero Page

5 8. A hang glider 25 meters above the ground starts to descend at a constant rate of 2 meters per second. Which equation shows the height h after t seconds of descent? A h = 25t + 2t B h = 5t + 2 C h = 2t + 25 D h = t + 25 D 9. GEOMETRY Two rectangular walls each with a length of 12 feet and a width of 23 feet need to be painted. It costs $0.08 per square foot for paint. How much will it cost to paint the walls? F $22.08 G $23.0 H $3.50 J $.16 J 50. SHORT RESPONSE Maddie works at Game Exchange. They are having a sale as shown. Her employee discount is 15%. If sales tax is 7.25%, how much does she spend for a total of video games? $ Solve A B 52. 5n + 6 = = 7 + 3c WORLD RECORDS In 1998, Winchell s House of Donuts in Pasadena, California, made the world s largest donut. It weighed 5000 pounds and had a circumference of feet. What was the donut s diameter to the nearest tenth? (Hint: C = πd) 95.0 ft C D 10 A esolutions Manual - Powered by Cognero Page 5

6 59. ZOO At a zoo, the cost of admission is posted on the sign. Find the cost of admission for two adults and two children. Translate each sentence into an equation. 66. Twice a number t decreased by eight equals seventy. 2t 8 = Five times the sum of m and k is the same as seven times k. $3 Find the value of n. Then name the property used in each step n = 25 1; Multiplicative Identity 61. n 1 = 2 2; Multiplicative Identity n = ; Reflexive Property 63. n + 0 = 6. ; Additive Identity 1; Multiplicative Inverse 65. (10 8)(7) = 2(n) 7; Transitive Property 5(m + k) = 7k 68. Half of p is the same as p minus 3. p = p 3 Evaluate each expression ( 1) (20) (1) ( 5) ( 5) 125 esolutions Manual - Powered by Cognero Page 6

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