150 Chapter 3 Solving Equations The x coefficient is now 1, because equals 1. Example 2 x 4 x 4 5 4 152 x 20 5 The solution is 20. Check: ✓ True b. x 4 1202 4 5 To isolate t, multiply both sides by 8. Regroup factors. The coefficient on t is now 1. 4 8 122 8 16 8 8 t 8 16 t The solution is 16 and checks in the original equation. 2. Comparing the Properties of Equality It is important to determine which property of equality should be used to solve an equation. For example, compare equations: 4 x 12 and 4x 12 In the first equation, the operation between 4 and x is addition. Therefore, we want to reverse the process by subtracting 4 from both sides. In the second equation, the operation between 4 and x is multiplication. To isolate x, we reverse the process by dividing by 4. 4 x 12 4x 12 4x 4 12 4 4 4 x 12 4 x 8 x 3 16 1 t t 2 t 8 5 5 44 1x 20 Answers 4. 18 5. 50 Applying the Multiplication Property of Equality Solve the equations. a. b. Solution: a. To isolate x, multiply both sides by 4. Regroup factors. 4 4 x 20 2 t 8 x 4 5 Skill Practice Solve the equations. 4. 5. 5 w 10 y 6 3
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