Section 3.4 Solving Equations with Multiple Steps 155 Answers 3. 36 4. 10 Solving a Linear Equation Solve. Solution: Simplify. Simplify.The solution is 12. Check: Substitute 12 for y. 14 14 y 2 8 1122 2 8 14 6 8 ✓ True 2 6 2 12 y y 2 6 y 2 14 8 y 2 8 8 14 y 2 8 14 y 2 8 Example 3 Subtract 8 from both sides. This will isolate the term containing the variable, y. Multiply both sides by 2 to make the y coefficient equal to 1. Skill Practice Solve. 3. 3 x 3 9 In Example 4, the variable x appears on both sides of the equation. In this case, apply the addition or subtraction properties of equality to collect the variable terms on one side of the equation and the constant terms on the other side. Solving a Linear Equation with Variables on Both Sides Solve. 4x 5 2x 13 Solution: To isolate x, we must first “move” all x terms to one side of the equation. For example, suppose we add 2x to both sides.This would “remove” the x term from the right-hand side because 2x 2x 0.The term 2x is then combined with 4x on the left-hand side. Add 2x to both sides. Simplify. Next, we want to isolate the term containing x. Subtract 5 from both sides to isolate the x term. Simplify. Divide both sides by 6 to obtain an x coefficient of 1. The solution is 3 and checks in the original equation. 4x 5 2x 13 4x 2x 5 2x 2x 13 6x 5 13 6x 5 5 13 5 6x 18 6x 6 x 3 18 6 Example 4 Skill Practice Solve. 4. 8y 3 6y 17 Avoiding Mistakes Remember to rewrite subtraction as addition of the opposite to perform calculations. 13 5 13 (5) 18
miller_prealgebra_2e_ch1_3
To see the actual publication please follow the link above