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- In Exercises 1–6, solve for x.In Exercises 23–25, solve each equation. If the solution set is Ø or (-0, ), classify the equation as an inconsistent equation or an identity. 23. 3(2x – 4) = 9 – 3(x + 1) 2x 24. x - 4 x + 1 4 2 4 25. 3(x – 4) + x = 2(6 + 2x)In Exercises 27–42, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 27. I = Prt for P 28. C = 2ar for r 30. P = C + MC for M 32. A = th(a + b) for b 29. T = D + pm for p 31. A = h(a + b) for a %3D 33. S = P + Prt for r 34. S = P + Prt for t F for S S - V C 36. S = 35. В %3D 1 -r 37. IR + Ir = E for I 38. A = 2lw + 2lh + 2wh for h 1 1 39. - + 1 1 40. R R R 1 =- for f for R fih -for fi fi + 2 fifz for f2 fi + 2 41. f = 42. f =
- In Exercises 43–54, solve each absolute value equation or indicate the equation has no solution. 43. |x – 2| = 7 45. |2x – 1| = 5 47. 2|3x – 2| = 14 44. |x + 1| = 5 46. |2r – 3| = 11 48. 3|2x – 1| = 21 %3D %3D 5 24 - + 6 = 18 50. 4 1 x + 7 = 10 51. |x + 1| + 5 = 3 53. |2x – 1| + 3 = 3 52. |x + 1| + 6 = 2 54. |3x – 2| + 4 = 4For Exercises 33–38, find the exact value of each expression without the use of a calculator. (See Example 5)In Exercises 49–54, solve for y in terms of t or x, as appropriate.
- For Exercises 101–104, verify by substitution that the given values of x are solutions to the given equation. 101. x + 25 = 0 102. x + 49 = 0 a. x = 5i a. x = 7i b. x = -5i b. x = -7i 103. x - 4x + 7 = 0 104. x - 6x + 11 = 0 a. x = 2 + iV3 b. x = 2 – iV3 a. x = 3 + iVā b. x = 3 – iV2In Exercises 59–64, solve and check each linear equation. 59. 2x – 5 = 7 60. 5x + 20 = 3x 61. 7(x – 4) = x + 2 62. 1 - 2(6 – x) = 3x + 2 63. 2(x – 4) + 3(x + 5) = 2x – 2 64. 2x 4(5x + 1) = 3x + 17For Exercises 33–42, solve the equation on the interval [0, 2π). (See Examples 5–7)