Section 2.2 The Addition Property of Equality 109 Solving equations is a critical skill that we need in algebra. At this level, the calculator should be only used to check our work. Two methods were shown in Section 2.1 as to how the calculator can be used to verify solutions. Another method is shown next. Example: Verify that x = -14 is a solution of x + 4 = -10. Solution: Store the value of x into the calculator. Enter the equation and press enter. If “1” is displayed, the statement is true for the stored value of x and this value is a solution of the equation. If “0” is displayed, the statement is false for the stored value of x and this value is not a solution of the equation. ( ) 1 4 T u n ENTER T T u n + 4 2nd MATH 1 ( ) 1 ENTER Because a 1 is displayed, x = -14 is a solution of x + 4 = -10. GRAPHING CALCULATOR SKILLS SECTION 2.2 EXERCISE SET Write About It! Use complete sentences to explain the meaning of the given term or process. 1. Linear equation in one variable 2. The addition property of equality 3. Solving a linear equation using the addition property of equality 4. The solution of an equation Determine if each statement is true or false. If a statement is false, explain why. 5. To isolate the variable term in the equation 7 + x = -4, add 4 to both sides of the equation. 6. To isolate the variable term in the equation -5x = 2, add 5 to both sides of the equation. 7. In the equation -5x = -6x + 4, the variable term on the right side of the equation can be eliminated by adding 6x to both sides. 8. In the equation 7x = 9x - 14, the variable term on the right side of the equation can be eliminated by adding 9x to both sides. Practice Makes Perfect! Decide if each equation is linear. If the equation is not linear, explain why. (See Objective 1.) 9. 2x - 5 = 0 10. 3(4x + 5) - 7 = 2(x + 1) 11. 2x2 - x + 1 = 3 12. -4x2 + 3x + 5 = 0 13. 1 5 x - 3 + 4 5 x = 7 14. 1 2 x - 5=- 1 2 x + 2 Use the addition property of equality to solve each equation. Remember to check each solution. (See Objective 2.) 15. x + 3 = -5 16. y + 8 = -1 17. b - 7 = -3 18. a - 1 = -10 19. x - 3 = 3 20. x + 12 = 12 21. -3 = x - 4 22. 10 = 5 + x 23. x + 6 7 =- 1 7 24. x - 3 4 = 5 4 25. y + 2.5 = .5 26. b - 5.4 = 5 27. 6.5 + c = 2.4 28. -4.2 + a = -7.3 Solve each equation. (See Objective 3.) 29. 5 - x + 2x - 4 = 7 30. -3y + 7 + 4y - 10 = -3 31. -9 - 6y - 7 + 7y = 10 - 13 32. 8b + 11 - 7b - 12 = -7 - 5 33. 3x + 6 = 2x - 5 34. 5x - 7 = 4x - 6 35. -2x - 3 = -3x + 4 36. -5y + 1 = -6y + 2 37. 4 3 x - 5 = 1 3 x + 2 38. 7 6 x - 7 = 1 6 x + 2 39. 1.5a + 4 = 0.5a + 2 40. 2.4y + 3 = 1.4y - 7 41. 4(2x + 6) = 7x - 4 42. 3(4x - 5) = 11x + 20 43. 3(2x - 1) - 5(x + 3) = 0 44. 7(4x + 2) - 9(3x - 1) = 0 45. 6 5 (x - 10) = 1 5 (x + 5) 46. 5 4 ( y - 8) = 1 4 ( y + 8)
hendricks_beginning_intermediate_algebra_1e_ch1_3
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