SECTION 2.2 The Multiplication Property of Equality^93

In , we must change 3xto 1x, or x. To do this, we multiply each side of

the equation by , the reciprocal of 3, because

Multiply each side by

Associative property

Multiplicative inverse property

x= 5 Multiplicative identity property

1 x= 5

a

1

3

3 bx=^1

3

15

1

3.

1

3

13 x 2 =

1

3

15

3 x= 15

1

3

3 =^3

3 =1.

1

3

3 x= 15

The solution is 5. We can check this result in the original equation.

Just as the addition property of equality permits subtractingthe same number

from each side of an equation, the multiplication property of equality permits

dividingeach side of an equation by the same nonzero number.

Divide each side by 3.

x= 5 Same result as above

3 x

3

=

15

3

3 x= 15

The product of a

number and its

reciprocal is 1.

We can divide each side of an equation by the same nonzero number without

changing the solution. Do not, however, divide each side by a variable, since the

variable might be equal to 0.

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. For

example, to solve

it is easier to multiply by than to divide by

On the other hand, to solve

5 x= 20, it is easier to divide by 5 than to multiply by^15.

3

4.

4

3

3

4 x= 12,

NOW TRY
EXERCISE 1
Solve. 8 x= 80

Applying the Multiplication Property of Equality

Solve

5 x

5 =

5

x = 12 5 x= 1 x=x

5 x

5

=

60

5

5 x= 60

5 x= 60.

EXAMPLE 1

Divide each side by 5,

the coefficient of x.

CHECK Substitute 12 for xin the original equation.

Original equation

Let

✓ True

Since a true statement results, the solution set is 5126. NOW TRY

60 = 60

51122  60 x=12.

5 x= 60

Our goal is

to isolate x.

Dividing by 5 is the same

as multiplying by.^15

NOW TRY ANSWER

1. 5106