# Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1

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``