116 Chapter 2 Linear Equations and Inequalities Solving a Linear Equation Example 6 Solve the equation. Solution: 2 7x 5 61x 32 2x Step 1: Add like terms on the left. Clear parentheses on the right. Combine like terms. Step 2: Subtract 7x from both sides. Simplify. Step 3: Subtract 18 from both sides. 2 7x 5 61x 32 2x 3 7x 6x 18 2x 3 7x 8x 18 3 7x 7x 8x 7x 18 3 x 18 3 18 x 18 18 21 x x 21 The solution set is {21}. Step 5: The check is left to the reader. Skill Practice Solve the equation. 6. 412y 12 y 6y 3 y Solving a Linear Equation Example 7 Solve the equation. Solution: 9 1z 32 4z 4z 51z 22 6 Step 1: Clear parentheses. Combine like terms. Step 2: Add z to both sides. Step 4: Divide both sides by 4. Step 5: The check is left for the reader. 9 1z 32 4z 4z 51z 22 6 9 z 3 4z 4z 5z 10 6 12 3z z 16 12 3z z z z 16 12 4z 16 12 12 4z 16 12 4z 28 4z 4 28 4 z 7 The solution set is {7}. Skill Practice Solve the equation. 7. 10 1x 52 3x 6x 51x 12 3 Answers 6. e 7. {3} 7 4 f Step 4: Because the coefficient of the x term is already 1, there is no need to apply the multiplication or division property of equality. Step 3: Subtract 12 from both sides. Avoiding Mistakes When distributing a negative number through a set of parentheses, be sure to change the signs of every term within the parentheses.
miller_beginning_intermediate_algebra_4e_ch1_3
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