Section 1.1Solving Simple Equations 9In Exercises 31– 38, solve the equation. Check your solution.31. 3 — 2 + t 1 — 2 32. b 3 — 16 5 — 16 33. 3 — 7 m 6 34. 2 — 5 y 435. 5.2 a 0.4 36. f + 3π 7π37. 108π6πj 38. x (2) 1.4ERROR ANALYSIS In Exercises 39 and 40, describe and correct the error in solving the equation. 39. −0.8 r = 12.6 r = 12.6 (−0.8) r = 11.8
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40. − m — 3 = −43 ⋅ ( − m — 3 ) = 3 ⋅ (−4) m = −12
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41. ANALYZING RELATIONSHIPS A baker orders 162 eggs.Each carton contains 18 eggs. Which equation can you use to  nd the number x of cartons? Explain your reasoning and solve the equation. ○A162x 18 ○B x — 18 162 ○C18x 162 ○D x + 18 162MODELING WITH MATHEMATICS In Exercises 42– 44, write and solve an equation to answer the question. (See Examples 3 and 4.) 42. The temperature at 5 .. is 20°F. The temperature at 10 .. is 5°F. How many degrees did the temperature fall? 43. The length of an American ag is 1.9 times its width. What is the width of the ag?9.5 ft44. The balance of an investment account is $308 more than the balance 4 years ago. The current balance of the account is $4708. What was the balance 4 years ago? 45. REASONING Identify the property of equality that makes Equation 1 and Equation 2 equivalent.Equation 1 x 1 — 2 x — 4 + 3Equation 2 4x 2 x + 12 46. PROBLEM SOLVING Tatami mats are used as a oor covering in Japan. One possible layout uses four identical rectangular mats and one square mat, as shown. The area of the square mat is half the area of one of the rectangular mats.Total area 81 ft2 a. Write and solve an equation to  nd the area of one rectangular mat. b. The length of a rectangular mat is twice the width. Use Guess, Check, and Revise to nd the dimensions of one rectangular mat. 47. PROBLEM SOLVING You spend $30.40 on 4 CDs. Each CD costs the same amount and is on sale for 80% of the original price. a. Write and solve an equation to nd how much you spend on each CD. b. The next day, the CDs are no longer on sale. You have $25. Will you be able to buy 3 more CDs? Explain your reasoning. 48. ANALYZING RELATIONSHIPS As c increases, does the value of x increase, decrease, or stay the same for each equation? Assume c is positive.EquationValueof xx c 0cx 1cx c x — c 1