Algebra 1 Common Core Student Edition, Grade 8-9

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