112 Chapter 2 Linear Equations and Inequalities Section 2.2 Solving Linear Equations 1. Linear Equations Involving Multiple Steps In Section 2.1, we studied a one-step process to solve linear equations by using the addition, subtraction, multiplication, and division properties of equality. In Example 1, we solve the equation 2w 7 11. Solving this equation will require multiple steps.To understand the proper steps, always remember that the ultimate goal is to isolate the variable. Therefore, we will first isolate the term containing the variable before dividing both sides by 2. Solving a Linear Equation Example 1 Solve the equation. Solution: 2w 7 11 Add 7 to both sides of the equation.This isolates the w-term. 2w 7 11 2w 7 7 11 7 Check: 2w 18 2w 2 18 2 w 9 2w 7 11 2192 7 11 w 9 Substitute in the original equation. ✔ True. 18 7 11 11 11 The solution set is {9}. Skill Practice Solve the equation. 1. 5y 5 10 Solving a Linear Equation Solve the equation. Solution: Subtract 3 from both sides.This isolates the x-term. 1 5 1 x Simplify. 2 3 1 5 x 3 3 2 1 5 x 3 2 1 5 x 3 Example 2 Concepts 1. Linear Equations Involving Multiple Steps 2. Procedure for Solving a Linear Equation in One Variable 3. Conditional Equations, Identities, and Contradictions Answer 1. {3} Next, apply the division property of equality to obtain a coefficient of 1 for w. Divide by 2 on both sides.
miller_beginning_intermediate_algebra_4e_ch1_3
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