1. 2
Equations, Inequalities, and Applications

2. 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.

3. 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.

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

5. 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

6. 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 

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

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