154 Chapter 3 Solving Equations 2x 3 15 2192 3 15 Example 1 2x 3 3 15 3 2x 18 2x 2 As Example 1 shows, we will generally apply the addition (or subtraction) property of equality to isolate the variable term first. Then we will apply the multiplication (or division) property of equality to obtain a coefficient of 1 on the variable term. Solving a Linear Equation Example 2 Solve. 22 3c 10 Solution: We first isolate the term containing the variable by subtracting 10 from both sides. Subtract 10 from both sides because 10 10 0. The term containing c is now isolated. Divide both sides by 3 to make the c coefficient equal to 1. Simplify.The solution is 4. Check: Original equation Substitute 4 for c. 22 3c 10 22 3142 10 22 12 10 ✓ True 22 10 3c 10 10 12 3c 12 3 3c 3 4 c Solving a Linear Equation Solve. 2x 3 15 Solution: Remember that our goal is to isolate x. Therefore, in this equation, we will first isolate the term containing x.This can be done by adding 3 to both sides. Add 3 to both sides, because 3 3 0. The term containing x is now isolated (by itself).The resulting equation now requires only one step to solve. Simplify.The solution is 9. Check: Original equation Substitute 9 for x. 18 3 15 ✓ True x 9 18 2 Divide both sides by 2 to make the x coefficient equal to 1. Skill Practice Solve. 1. 3x 7 25 Skill Practice Solve. 2. 12 5t 13 Answers 1. 6 2. 5
miller_prealgebra_2e_ch1_3
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