2 Equations, Inequalities, and Applications

2.2 The Multiplication Property of Equality Objectives 1. Use the multiplication property of equality. 2. Simplify, and then use the multiplication property of equality.

Use the Multiplication Property of Equality If A, B, and C (C is not equal to 0) represent real numbers, then the equations A = B and AC = BC are equivalent equations. In words, we can multiply each side of an equation by the same nonzero number without changing the solution.

Using the Multiplication Property of Equality Example 1 Solve. 3x = 42 Divide each side by 3. x = 14 Check: 3 · 14 = 42 

Use the Multiplication Property of Equality Note In practice, it is usually easier to multiply on each side if the coefficient of the variable is a fraction, and divide on each side if the coefficient is an integer or a decimal. For example, to solve it is easier to multiply by the reciprocal of than to divide by On the other hand, to solve 5x = 20, it is easier to divide by 5 than to multiply by

Using the Multiplication Property of Equality Example 3 Solve. –1.5y = 7.5 Divide both sides by –1.5. y = –5 Check: –1.5 · –5 = 7.5 

Using the Multiplication Property of Equality Example 5 Solve. Multiply each side by the reciprocal. 

Combining Like Terms When Solving Example 7 Solve. 5a – 13a = 56 – 8a = 56 First combine like terms. Then solve. a = –7