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156 Chapter 3 Solving Equations Answer 5. 4 TIP: It should be noted that the variable may be isolated on either side of the equation. In Example 4 for instance, we could have isolated the x term on the righthand side of the equation. Subtract 4x from both sides. This “removes” the x term from the left-hand side. Add 13 to both sides to isolate the x term. Simplify. Divide both sides by 6. 4x 5 2x 13 4x 4x 5 2x 4x 13 5 6x 13 5 13 6x 13 13 18 6x 18 6 6x 6 3 x This is the same solution as in Example 4. 2. General Procedure to Solve a Linear Equation In Examples 1–4, we used multiple steps to solve equations. We also learned how to collect the variable terms on one side of the equation so that the variable could be isolated. The following procedure summarizes the steps to solve a linear equation. Solving a Linear Equation in One Variable Step 1 Simplify both sides of the equation. • Clear parentheses if necessary. • Combine like terms if necessary. Step 2 Use the addition or subtraction property of equality to collect the variable terms on one side of the equation. Step 3 Use the addition or subtraction property of equality to collect the constant terms on the other side of the equation. Step 4 Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1. Step 5 Check the answer in the original equation. Solving a Linear Equation Example 5 Solve. 21y 102 8 4y Solution: Step 1: Simplify both sides of the equation. Clear parentheses. Step 2: Add 4y to both sides to collect the variable terms on the left. 21y 102 8 4y 2y 20 8 4y 2y 4y 20 8 4y 4y 6y 20 8 Simplify. Skill Practice Solve. 5. 61z 4216 4z


miller_prealgebra_2e_ch1_3
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