Section 3.4 Solving Equations with Multiple Steps 157 Step 3: Subtract 20 from both sides to collect the constants on the right. Simplify. Step 4: Divide both sides by 6 to obtain a coefficient of 1 on the y term The solution is 2. 6y 20 20 8 20 6y 12 6y 6 y 2 Check: Step 5: Check the solution in the original equation. Substitute 2 for y. 21y 102 8 4y 212 102 8 4122 2182 8 182 16 16 ✓ The solution checks. 12 6 Answer 6. 44 Solving a Linear Equation Solve. 2x 3x 2 413 x2 Solution: Step 1: Simplify both sides of the equation. On the left, combine like terms. On the right, clear parentheses. Step 2: Subtract 4x from both sides to collect the variable terms on the left. Simplify. Step 3: Subtract 2 from both sides to collect the constants on the right. Step 4: The x coefficient is already 1.The solution is 14. 2x 3x 2 413 x2 5x 2 12 4x 5x 4x 2 12 4x 4x x 2 12 x 2 2 12 2 x 14 Check: 2x 3x 2 413 x2 Step 5: Check in the original equation. Substitute 14 for x. 21142 31142 2 433 1142 4 28 42 2 41172 70 2 68 68 68 ✓ The solution checks. Example 6 Skill Practice Solve. 6. 3y y 4 51y 82 TIP: A linear equation in one variable has one unique solution. As you continue your study of algebra you will also encounter equations that may have no solution or infinitely many solutions.
miller_prealgebra_2e_ch1_3
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