111 1.1 Linear Equations Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b). 39. V = lwh, for l (volume of a rectangular box) 40. I = Prt, for P (simple interest) 41. P = a + b + c, for c (perimeter of a triangle) 42. P = 2l + 2w, for w (perimeter of a rectangle) 43. = 1 2 h1B + b2, for B (area of a trapezoid) 44. F = GMm r2 , for m (force of gravity) 45. S = 2prh + 2pr2, for h (surface area of a right circular cylinder) 46. s = 1 2 gt2, for g (distance traveled by a falling object) 47. S = 2lw + 2wh + 2hl, for h (surface area of a rectangular box) 48. z = x - m s , for x (standardized value) Simple Interest Work each problem. See Example 5. 59. Elmer borrowed $3150 from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4%. (a) How much will the interest amount to? (b) What amount must Elmer pay Julio at the end of the 6 months? 60. Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%. (a) How much must she pay the bank in 18 months? (b) How much of the amount in part (a) is interest? Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 3. 31. 412x + 72 = 2x + 22 + 312x + 22 32. 1 216x + 202 = x + 4 + 21x + 32 33. 21x - 82 = 3x - 16 34. -81x + 52 = -8x - 51x + 82 35. 41x + 72 = 21x + 122 + 21x + 12 36. -612x + 12 - 31x - 42 = -15x + 1 37. 0.31x + 22 - 0.51x + 22 = -0.2x - 0.4 38. -0.61x - 52 + 0.81x - 62 = 0.2x - 1.8 Solve each equation for x. See Example 4(c). 49. 21x - a2 + b = 3x + a 50. 5x - 12a + c2 = 41x + c2 51. ax + b = 31x - a2 52. 4a - ax = 3b + bx 53. x a - 1 = ax + 3 54. x - 1 2a = 2x - a 55. a2x + 3x = 2a2 56. ax + b2 = bx - a2 57. 3x = 12x - 121m+ 42 58. -x = 15x + 3213k + 12 29. 0.08x + 0.061x + 122 = 7.72 30. 0.041x - 122 + 0.06x = 1.52
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