144 Chapter 3 Solving Equations In Example 2, the addition property of equality was used to add a positive number to both sides of an equation to isolate the variable. In Section 2.3 we learned that addition of a negative number is equivalent to subtraction. This is the basis for using the subtraction property of equality for the equations in Example 3. Applying the Subtraction Property of Equality Example 3 Solve the equations and check. a. z 11 14 b. 8 2 q Solution: a. z 11 14 We can isolate z by adding 11 to both sides. Since adding 11 is the same as subtracting 11, we use the subtraction property of equality. To isolate z, subtract 11 from both sides, because 11 11 0. Simplify. The solution is 3. Check: Original equation Substitute 3 for z. ✓ True z 11 11 14 11 z 0 3 z 3 b. 8 2 q z 11 14 132 11 14 14 14 To isolate q, subtract 2 from both sides, because 2 2 0. On the left side, change subtraction to addition of the opposite. Simplify. The solution is 10. Check: Original equation Substitute 10 for q. 8 2 q 8 2 1102 ✓ True 8 8 8 2 2 2 q 8 122 0 q 10 0 q 10 q The equations in Example 4 require that we simplify the expressions on both sides of the equation, then apply the addition or subtraction property as needed. As you read through each example, remember that you want to isolate the variable. Skill Practice Solve the equation and check the solution. 8. m 8 21 9. 16 1 z Answers 8. 13 9. 17
miller_prealgebra_2e_ch1_3
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