164 CHAPTER 1 Equations and Inequalities CONCEPT PREVIEWMatch each equation in Column I with the correct first step for solving it in Column II. I 6. 2x + 3 x + 5 x + 5 = 7 7. 2x + 5 = 7 8. 1x + 525/2 = 32 9. 1x + 522/3 - 1x + 521/3 - 6 = 0 10. 23 x1x + 52 = 23 -6 II A. Cube each side of the equation. B. Multiply each side of the equation by x1x + 52. C. Raise each side of the equation to the power 2 5. D. Square each side of the equation. E. Let u = 1x + 521/3 and u2 = 1x + 522/3. Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. See Examples 1 and 2. 11. 5 2x + 3 - 1 x - 6 = 0 12. 2 x + 1 + 3 5x - 2 = 0 13. 3 x - 2 + 1 x + 1 = 3 x2 - x - 2 14. 2 x + 3 - 5 x - 1 = -5 x2 + 2x - 3 15. 1 4x - 2 x = 3 16. 5 2x + 2 x = 6 Solve each equation. See Example 1. 17. 2x + 5 2 - 3x x - 2 = x 18. 4x + 3 4 - 2x x + 1 = x 19. x x - 3 = 3 x - 3 + 3 20. x x - 4 = 4 x - 4 + 4 21. -2 x - 3 + 3 x + 3 = -12 x2 - 9 22. 3 x - 2 + 1 x + 2 = 12 x2 - 4 23. 4 x2 + x - 6 - 1 x2 - 4 = 2 x2 + 5x + 6 24. 3 x2 + x - 2 - 1 x2 - 1 = 7 2x2 + 6x + 4 Solve each equation. See Example 2. 25. 2x + 1 x - 2 + 3 x = -6 x2 - 2x 26. 4x + 3 x + 1 + 2 x = 1 x2 + x 27. x x - 1 - 1 x + 1 = 2 x2 - 1 28. -x x + 1 - 1 x - 1 = -2 x2 - 1 29. 5 x2 - 43 x = 18 30. 7 x2 + 19 x = 6 31. 2 = 3 2x - 1 + -1 12x - 122 32. 6 = 7 2x - 3 + 3 12x - 322 33. 2x - 5 x = x - 2 3 34. x + 4 2x = x - 1 3 35. 2x x - 2 = 5 + 4x2 x - 2 36. 3x2 x - 1 + 2 = x x - 1
RkJQdWJsaXNoZXIy NjM5ODQ=