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- For Exercises 49–52, rewrite the equation so that the coefficient on x is positive.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 49–54, solve for y in terms of t or x, as appropriate.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)
- 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 – iV2For Exercises 33–42, solve the equation on the interval [0, 2π). (See Examples 5–7)America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?