Objective 22Solve one-step equations,

multiply and divide

©2002 by R. Villar

All Rights Reserved

Solve one-step equations, multiply and divideIn the last section we used addition to undo subtraction

and we used subtraction to undo addition.

Addition and subtraction are called inverse operations of each other.

In this section we will use multiplication and division to undo each other since they are inverse operations of each other.

Example: Solve 112 = –14nTo “undo” multiplication, we will use division... The opposite of multiplying by –14 is dividing by –14. –14 –14

The –14’s will cancel leaving n by itself...

–8 = n

Check the original problem... 112 = –14(–8) √

Example: Solve 3 = z 9.5

To undo division, we will use multiplication...

3 • 9.5 = z • 9.5 9.5

28.5 = z

Check: 3 = 28.5 √ 9.5

Example: Solve

To undo multiplication of fractions, we can use the reciprocal.

We will first convert the mixed number into an improper fraction...

x = – 9916

Check: √

€

23x = −4

18

€

23x = −

338

Now, multiply both sides by the reciprocal of 2/3...

€

32

• • 32

The reciprocals will cancel leaving x on the left side...Multiply the right side to solve for x...

€

23

−9916

⎛ ⎝

⎞ ⎠ = −

338