Applying the Multiplication Property of Equality

Solve

Multiply each side by , the reciprocal of.

Multiplicative inverse property

Check to confirm that the solution set is 586. NOW TRY

w= 8

1 #w=

4

3

#^6

1

3

4

4

3

4

3

3

4

w=

4

3

6

3

4

w= 6

3

4 w=6.

EXAMPLE 5

SECTION 2.2 The Multiplication Property of Equality 95

NOW TRY
EXERCISE 5
Solve.^47 z=- 16

NOW TRY
EXERCISE 6
Solve .-x= 9

NOW TRY
EXERCISE 7
Solve. 9 n- 6 n= 21

Multiplicative identity property;

multiply fractions.

In Section 2.1,we obtained in our alternative solution to Example 4.

We reasoned that since the additive inverse (or opposite) of xis , then xmust

equal 17. We can use the multiplication property of equality to obtain the same result.

- 17

- x=- 17

Applying the Multiplication Property of Equality

Solve

Multiply each side by.

Associative property; multiply.

Multiplicative inverse property

Multiplicative identity property

CHECK Original equation

Let

✓ True

The solution, 17, checks, so 5176 is the solution set. NOW TRY

- 17 =- 17

- 1172 - 17 x=17.

- x=- 17

x= 17

1 x= 17

3 - 11 - 124 x= 17

- 11 - 1 x 2 = - 11 - 172 - 1

- 1 x=- 17 - x=- 1 x

- x=- 17

- x=-17.

EXAMPLE 6

These steps are

usually omitted.

OBJECTIVE 2 Simplify, and then use the multiplication property of equality.

Combining Like Terms When Solving

Solve

Combine like terms.

Divide by 11.

Multiplicative identity property; divide.

CHECK Original equation

Let.

Multiply.

✓ True

Since a true statement results, the solution set is 536. NOW TRY

33 = 33

15 + 18  33

5 132 + 6 132  33 m= 3

5 m+ 6 m= 33

m= 3

11 m

11

=

33

11

11 m= 33

5 m+ 6 m= 33

5 m+ 6 m= 33.

EXAMPLE 7

NOW TRY ANSWERS

5. 5 - 286 6. 5 - 96 7. 576