148 Chapter 3 Solving equations Section 3.3 Multiplication and Division Properties 1. Multiplication and Division Properties of Equality Adding or subtracting the same quantity on both sides of an equation results in an equivalent equation. The same is true when we multiply or divide both sides of an equation by the same nonzero quantity. Multiplication and Division Properties of Equality Let a, b, and c represent algebraic expressions, where c 0. 1. The multiplication property of equality: If a b, then, c a c b 2. The division property of equality: If a b then, To understand the multiplication property of equality, suppose we start with a true equation such as 10 10. If both sides of the equation are multiplied by a constant such as 3, the result is also a true statement (Figure 3-2). 3 10 lb 3 10 lb 10 lb Figure 3-2 10 lb 10 lb 10 10 3 10 3 10 To solve an equation in the variable x, the goal is to write the equation in the form x number. In particular, notice that we want the coefficient of x to be 1. That is, we want to write the equation as 1 x number. Therefore, to solve an equation such as 3x 12, we can divide both sides of the equation by the 3.We do this because , and that leaves 1x on the left-hand side of the equation. Divide both sides by 3. The coefficient of the x term is now 1. 33 1 3x 12 3x 3 12 3 1 x 4 x 4 Simplify. 10 lb 10 lb 10 lb 10 lb 10 lb a c b c 30 30 TIP: Recall that the quotient of a nonzero number and itself is 1. For example: and 5 5 1 3 3 1 of Equality Concepts 1. Multiplication and Division Properties of Equality 2. Comparing the Properties of Equality
miller_prealgebra_2e_ch1_3
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