Section 3.3 Multiplication and Division Properties of Equality 151 To solve each equation, we want to isolate the variable. If the operation between a term and the variable is addition or subtraction, we apply the subtraction or addition property of equality. If the variable is multiplied or divided by a constant, then we apply the division or multiplication property of equality. In Example 3, we practice distinguishing which property of equality to use. Solving Linear Equations Example 3 Solve the equations. a. b. x 18 2 c. 20 8 10t 3t d. 4 10 4t 31t 22 1 Solution: a. The operation between m and 12 is division. To obtain a coefficient of 1 for the m term, multiply both sides by 12. Multiply both sides by 12. Regroup. Simplify both sides. The solution 36 checks in the original equation. m 12 m 12 3 12132 m 36 12 12 12 b. x 18 2 The operation between x and 18 is addition. To isolate x, subtract 18 from both sides. Subtract 18 on both sides. Simplify.The solution is 16 and checks in the original equation. x 18 18 2 18 x 16 c. 20 8 10t 3t Begin by simplifying both sides of the equation. 28 7t The relationship between t and 7 is multiplication. To obtain a coefficient of 1 on the t term, we divide both sides by 7. Divide both sides by 7. 4 t Simplify.The solution is 4 and checks in the original equation. d. 4 10 4t – 31t 22 1 Begin by simplifying both sides of the equation. 6 4t 3t 6 1 Apply the distributive property on the right-hand side. 6 t 7 Combine like terms on the right-hand side. 6 7 t 7 7 To isolate the t term, add 7 to both sides. This is because 7 7 0. 13 t The solution is 13 and checks in the original equation. 28 7 7t 7 m 12132 m 12 3 Skill Practice Solve the equations. 6. 8 7. x 46 12 8. 10 5p 7p 9. 5 20 3 6w 51w 12 t 5 Answers 6. 40 7. 34 8. 5 9. 23
miller_prealgebra_2e_ch1_3
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