How can you make

the equation easier

to solve?

Remove the grouping

symbols by using the

Distributive Property.

`Solving an Equation Using the Distributive Property`

What is the solution of — 8(2x — 1) = 36?

`-8 (2 *- 1) = 36`

Distributive Property

Subtract 8 from each side.

Simplify.

`Divide each side by -1 6.`

`Simplify.`

`— 1 6 x + 8 = 36`

— 1 6 x + 8 — 8 = 36 — 8

-1 6 x = 28

— 1 6 x 2 8

-16 -16

7

x=~4

`Got It? 3. a. W hat is th e solution of 18 = 3(2x - 6 )? Check your answer.`

b. Reasoning Can you solve th e eq u a tio n in p a rt (a) by using th e Division

P roperty of Equality instead of th e D istributive Property? Explain.

`Pt an`

How do you get

started?

You can e ith e r co m bine

like term s by w ritin g the

fra c tio n s w ith a com m on

de n om inator, o r you can

clear the fractions from

the equation.

`You can use different m eth o d s to solve equations th a t contain fractions.`

`Solving an Equation That Contains Fractions`

`What is the solution of | = 10?`

`Method 1 Write the like term s using a co m m o n d en o m in ato r a n d solve.`

3

4X-|x =^10 Rewrite the fractions.

9

12X - j^2 x =^10 Write the fractions using a common denominator, 12.

`EhX`

`III—*O Combine like terms.`

`¥(12X )^5 Multiply each side by y , the reciprocal of`

X= 24 Simplify.

`Method 2 Clear the fractions from th e equation.`

`(-3x 4 - - 3 I = 1 2 ( 1 0 ) M u lt ip ly ea ch s id e b y a c o m m o n d e n o m in a to r, 12.`

`12 (t) ~ 12 (f) = Distributive Property`

9x - 4x = 120 Multiply.

5x = 120 Combine like terms,

x = 2 4 D iv id e ea ch s id e b y 5 a n d s im p lify.

`96 Ch ap t er 2 So l v i n g Eq u a t i o n s`