Page 600 - Basic College Mathematics with Early Integers

8.3 SOLVING EQUATIONS: THE MULTIPLICATION PROPERTY Objective

Use the Multiplication Property
to Solve Equations.
Objective Using the Multiplication Property to Solve Equations
Although the addition property of equality is a powerful tool for helping us solve
equations, it cannot help us solve all types of equations. For example, it cannot help
us solve an equation such as 2x = 6. To solve this equation, we use a second prop-
erty of equality called the multiplication property of equality.

Multiplication Property of Equality

Let a, b, and c represent numbers and let c Z 0. Then
a = b Also, a = b
a b
#
#
and a c = b c and =
c c
are equivalent equations. are equivalent equations.

In other words, both sides of an equation may be multiplied or divided by the same
nonzero number without changing the solution of the equation.
Picturing again our balanced scale, if we multiply or divide the weight on each
side by the same nonzero number, the scale (or equation) remains balanced.

To solve 2x = 6 for x, we use the multiplication property of equality to divide
both sides of the equation by 2, and simplify as follows:
2x = 6
2x 6
= Divide both sides by 2.
2 2
2
# x = 3
2
#
1 x = 3
x = 3

Example 1 Solve: -5x = 15 PRACTICE 1
Solve: -3y = 18
Solution: To get x by itself, we divide both sides by -5.
-5x = 15 Original equation
-5x 15
= Divide both sides by -5 .
-5 -5
-5 15
# x =
-5 -5
#
1 x =-3 Simplify. Answer
x =-3 1. -6
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