106 Chapter 2 Linear Equations and Inequalities Applying the Multiplication Property of Equality Solve the equation by using the multiplication property of equality. Solution: To obtain a coefficient of 1 for the q-term, multiply by the reciprocal of , which is . Simplify. The product of a number and its reciprocal is 1. Check: The solution set is . ✔ True Skill Practice Solve the equation. 10. 2 3 a 1 4 1 3 1 3 e 3 2 f 2 9 a 3 2 b 1 3 2 9 q 1 3 q 3 2 1q 3 2 92 29 a 9 2 b a 2 9 qb 1 3 a 9 2 b 2 9 q 1 3 2 9 q 1 3 Example 5 Answer 10. e 3 8 f TIP: When applying the multiplication or division property of equality to obtain a coefficient of 1 for the variable term, we will generally use the following convention: • If the coefficient of the variable term is expressed as a fraction, we will usually multiply both sides by its reciprocal, as in Example 5. • If the coefficient of the variable term is an integer or decimal, we will divide both sides by the coefficient itself, as in Example 6. Applying the Division Property of Equality Solve the equation by using the division property of equality. Solution: To obtain a coefficient of 1 for the z-term, divide by Simplify. 3.43 0.7z 3.43 0.7 0.7z 0.7 0.7. 4.9 1z 4.9 z 3.43 0.7z Example 6
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