Example 2: Translate each equation into a sentence. a. 4n 8 = 12. – 4n 8 = 12 – Four times minus eight equals twelve. n Exercises: Translate each sentence into an equation or formula. 52. times a number minus twelve equals forty. 3t-12=40 t One–half of the difference of and is 54. 53. a b Three times the sum of and 4 is 32. 54. 3(d+4)=32 d Translate each equation into a sentence. 55. 4a 5 = 23 56. 10 + = 4k k – 57. 6xy = 24 58. + = 8 x2 y2 Lesson 2-2: Solving One-Step Equations For any numbers and if = then + = + Addition Property of Equality a, b, c, a b, a c b c. Subtraction Property of Equality For any numbers a, b, and c, if a = b, then a c = b c. – – Example 1: Solve 32 = 18. m – 32 = 18 m – Original equation 32 + 32 = 18 + 32 m – Add 32 to each side. = 50 m Simplify. The solution is 50. Example 2: Solve 22 + = p –12. 22 + = p –12 Original equation 22 + 22 = 22 p – –12 – Subtract 22 from each side. = p –34 Simplify. The solution is –34. Exercises Solve each equation. Check your solution. 59. 3 = 1 60. 5 = 15 20 61. 0.5 = 2.3 2.8 h p k – –2 – – 62. 18 = 1 63. 0.2 = 1.8 2 64. (–12) = 10 -2 h j m – –17 – – 65. + 12 = 63 51 66. = + 4 -21 67. = l + (– 0.2) -3 x b –17 –3.2 68. 19 + = 4 -23 69. + 1.2 = 2.8 1.6 70. + (–8) = 2 10 h j m – Multiplication Property of Equality For any numbers a, b, and c, if a = b, then ac = bc. Division Property of Equality For any numbers a, b, and c, with c 0, if a = b, then = . ≠ Example 1: = . = . Original equation
Example 2: Translate each equation into a sentence. a. 4n – 8 = 12. 4n – 8 = 12 Four times n minus eight equals twelve. Exercises: Translate each sentence into an equation or formula. 52. times a number t minus twelve equals forty. 3t-12=40 53. One–half of the difference of a and b is 54. 54. Three times the sum of d and 4 is 32. 3(d+4)=32 Translate each equation into a sentence. 55. 4a – 5 = 23 56. 10 + k = 4k 57. 6xy = 24 58. x2 + y2 = 8 Lesson 2-2: Solving One-Step Equations Addition Property of Equality For any numbers a, b, and c, if a = b, then a + c = b + c. Subtraction Property of Equality For any numbers a, b, and c, if a = b, then a – c = b – c. Example 1: Solve m – 32 = 18. m – 32 = 18 Original equation m – 32 + 32 = 18 + 32 Add 32 to each side. m = 50 Simplify. The solution is 50. Example 2: Solve 22 + p = –12. 22 + p = –12 Original equation 22 + p – 22 = –12 – 22 Subtract 22 from each side. p = –34 Simplify. The solution is –34. Exercises Solve each equation. Check your solution. 59. h – 3 = –2 1 60. p – 5 = 15 20 61. k – 0.5 = 2.3 2.8 62. h – 18 = –17 1 63. j – 0.2 = 1.8 2 64. m – (–12) = 10 -2 65. x + 12 = 63 51 66. –17 = b + 4 -21 67. –3.2 = l + (– 0.2) -3 68. 19 + h = – 4 -23 69. j + 1.2 = 2.8 1.6 70. m + (–8) = 2 10 Multiplication Property of Equality For any numbers a, b, and c, if a = b, then ac = bc. Division Property of Equality For any numbers a, b, and c, with c ≠ 0, if a = b, then = . Example 1: = . = . Original equation
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