98 Chapter 2 Linear Equations and Inequalities in One Variable Write About It! Use complete sentences in your answer to the following exercises. Provide a specifi c example of each term or process. 1. Explain the meaning of an equation. 2. Explain what it means for a number to be the solution of an equation. 3. Explain the process of verifying if a number is a solution of an equation. 4. Explain the difference between an expression and an equation. 5. Explain the difference between a numerical equation and an algebraic equation. 6. Explain the difference between the two statements: “4 less than a number” and “4 minus a number”. Practice Makes Perfect! Determine whether each of the following is an expression or an equation. (See Objective 1.) 7. 3x + 2 8. 4y + 6 = 3 9. 2x – 1 = –5 10. 2x – 1 11. –7x 12. 7x = 0 13. x2 - x - 6 = 0 14. x2 - x - 6 15. 3(x - 8) = 4 16. 3(x – 8) Determine if the given numbers are solutions of the equation. (See Objective 2.) 17. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x – 1 = –3? 18. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x + 1 = 0? 19. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of 3x = 0? 20. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of -2x = -4? 21. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x2 - x - 2 = 0? 22. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x2 + x - 2 = 0? 23. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x2 = 1? 24. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x2 = 2x? 25. Is x = –2, x = –1, x = 0, x = 1, or x = 2 a solution of x – 2 = x? 26. Is x = –2, x = –1, x = 0, x = 1, or x =2 a solution of 3x – 8 – x = 2(x – 4)? For each exercise, defi ne a variable and write an equation that can be used to solve the problem. (See Objective 3.) 27. The sum of a number and 4 is -3. 28. The sum of a number and -6 is 8. 29. The difference of a number and 7 is 4. 30. The difference of a number and 10 is -2. 31. Twice a number is 18. 32. Three times a number is -12. 33. The quotient of a number and 4 is 8. 34. The quotient of a number and 2 is –5. 35. The sum of twice a number and 7 is the same as one less than the number. 36. Two more than three times a number equals the number decreased by 9. 37. Three divided by a number gives the same result as one-third of the number. 38. The ratio of a number to 5 equals twice the number. 39. Four less than three times a number is six more than the number. 40. Six less than five times a number is two more than the number. 41. If three times a number is added to four times the same number, the result is the same as seven less than five times the number. 42. If twice a number is added to three times the same number, the result is the same as seven more than four times the number. 43. Four times the sum of a number and –2 is the same as twice the number. 44. Six times the difference of a number and –10 is the same as four times the number. 45. The difference of four times a number and -12 is equal to 50 more than the number. 46. The difference of twice a number and –7 is equal to 18 more than the number. 47. The sum of twice a number and 18 is equal to 27 less than the number. 48. The sum of eight times a number and 24 is equal to 32 less than the number. For each problem, defi ne a variable and write an equation that can be used to solve the problem. (See Objective 4.) 49. One angle is 13° less than another angle. Their sum is 90°. Find the measure of each angle. 50. One angle is 16° more than another angle. Their sum is 180°. Find the measure of each angle. SECTION 2.1 EXERCISE SET
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