Section 3.2 Addition and Subtraction Properties of Equality 143 Skill Practice Solve the equation and check the solution. 5. y 4 12 6. 18 w 5 7. 9 z 2 Answers 5. 16 6. 23 7. 11 Applying the Addition Property of Equality Solve the equations and check the solutions. a. x 6 18 b. 12 x 7 c. 4 y 5 Solution: To solve an equation, the goal is to isolate the variable on one side of the equation. That is, we want to create an equivalent equation of the form x number.To accomplish this, we can use the fact that the sum of a number and its opposite is zero. a. x 6 18 Rewrite subtraction as addition of the opposite. To isolate x, add 6 to both sides because 6 6 0. Simplify. The variable is isolated (by itself) on the lefthand side of the equation. The solution is 24. Check: Original equation Substitute 24 for x. ✓ True x 162 18 x 162 6 18 6 x 0 24 b. 12 x 7 x 6 18 1242 6 18 Rewrite subtraction as addition of the opposite. To isolate x, add 7 to both sides because 7 7 0. 12 x 172 5 x 0 Simplify. 5 x The variable is isolated on the right-hand side of the equation. The solution is 5. The equation 5 x is equivalent to x 5. Check: Original equation Substitute 5 for x. 12 x 7 12 152 7 ✓ True c. 4 y 5 12 12 4 4 y 5 4 To isolate y, add 4 to both sides, because 4 4 0. 0 y 9 Simplify. y 9 The solution is 9. Check: Original equation Substitute 9 for y. 4 y 5 4 192 5 5 5 ✓ True 12 7 x 172 7 18 18 x 24 Example 2 TIP: Notice that the variable may be isolated on either side of the equal sign. In Example 2(a), the variable appears on the left. In Example 2(b), the variable appears on the right. Avoiding Mistakes To check the solution to an equation, always substitute the solution into the original equation. Then independently evaluate the expression on each side of the equation.
miller_prealgebra_2e_ch1_3
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