xercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. A(n) – is a statement that two expressions are equal. 2. To an equation means to find all numbers that make the equation a true statement. 3. A linear equation is a(n) because the greatest degree of the variable is 1. 4. A(n) is an equation satisfied by every number that is a meaningful replace- ment for the variable. 5. A(n). is an equation that has no solution. CONCEPT PREVIEW Decide whether each statement is true or false. 6. The solution set of 2x + 5 = x – 3 is {-8}. 7. The equation 5(x – 8) = 5x – 40 is an example of an identity. 8. The equation 5x 4x is an example of a contradiction. 9. Solving the literal equation A = ; bh for the variable h gives h 2b• 10. CONCEPT PREVIE W Which one is not a linear equation? A. 5x + 7(x – 1) = -3x B. 9x2 - 4x + 3 = 0 C. 7x + 8x = 13x D. 0.04x - 0.08x = 0.40 %3D %3D Solve each equation. See Examples 1 and 2. 11. 5x + 4 = 3x - 4 12. 9x + 11 = 7x + 1 %3D (13, 6(3x – 1) = 8 – (10x – 14) 14. 4(-2x + 1) = 6 – (2x – 4) %3D 5 15. -x 4 5 4 - 2x+ 16. X + -x 5* 2 5* 3 3 4. 17. 3x + 5 – 5(x + 1) = 6x + 7 18. 5(x + 3) + 4.x - 3 = -(2x - 4)+ 2 19. 2[x - (4 + 2x) + 3] = 2x + 2 20. 4[2x – (3 - x) + 5] = -6x – 28 %3D x + 10 x + 2 (3x – (21(3x-2) = - (3х — 2) : (2x+5) 22. %3D 10 15 24. 0.01x + 3.1 = 2.03x - 2.96 23. 0.2x- 0.5 = 0.1x + 7 25. -4(2x- 6) + 8x = 5x + 24 + x 26. -8(3x + 4) + 6x = 4(x - 8) + 4x 4 27. 0.5x + x= x+ 10 3 28. x+ +.25x x+ 2 3 29. 0.08x + 0.06(x+ 12)= 7.72 30. 0.04(x - 12) + 0.06.x = 1.52 %3D Determine whether each equation is an identity, a conditional equation, or a contradic- tion. Give the solution set. See Example 3. 1 31. 4(2x + 7) = 2x + 22 + 3(2x + 2) 32. (6x + 20) = x + 4 + 2(x+ 3) (33) 2(x- 8) = 3x - 16 34. -8(x+ 5)= -8x – 5(x+ 8) %3D 35, 4(x+ 7) = 2(x + 12) + 2(x + 1) 36. –6(2x + 1) – 3(x – 4) = -15x + 1 %3D 37. 0.3(x + 2) – 0.5(x + 2) = -0.2x – 0.4 38. -0.6(x – 5) + 0.8(x – 6) = 0.2x – 1.8 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, (volume of a rectangular box) for l 40. I = Prt, (simple interest) for P 41. P = a + b + c, (perimeter of a triangle) for c 42. P = 21 + 2w, for w (perimeter of a rectangle) h(B + b), 43. A = (area of a trapezoid) for B h(B+ b), (area of a trapezoid) for h %3D 45. S= 2rrh + 2™r², (surface area of a right circular cylinder) for h 46. . 8t2, (distance traveled by a falling object) for g 281 47 S= 2lw + 2wh + 2hl, for h (surface area of a rectangular box) anillaboM b ns anoitilqgA SI anoitsup llqbA (standardized value) 48. z = for x Solve each equation for x. See Example 4(c). dong 50. 5x- (2a + c) = 4(x + c) 49, 2(x- a) + b = 3x + a lot od amoldog %3D 52. 4а - ах %3 3Ь + bx 31. ax + b = 3(x – a) x-1 = 2x- a 2a 54. - = ax + 3 53. 56. ax + b? = bx - a? 55. a'x + 3x = 2a? %3D %3D 58. -x = (5x + 3)(3k + 1) 57. 3x (2x- 1)(m + 4) Work each problem. See Example 5. Simple Interest 59. Elmer borowed $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 money in 18 months with simple annual interest of 5.5%. th (a) How much must she pay the bank in 18 months? (hì How much of the amount in part (a) is interest?