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

(Marvins-Underground-K-12) #1
``````Got It? 4. W hat is th e solution of each equation? Why did you choose th e m eth o d
you u sed to solve each equation?
_ , 3b _ „. I _ 5 _ m
5 4 — 9 — 6 3``````

Think
When you multiply a
decimal by 10 ", where
n is a p o sitive integer,
you can move the
decimal point n places
to th e rig h t. For example,
100(3.5) = 350.

``````You can clear decim als from an eq u a tio n by m ultiplying by a pow er of 10. First, find
the greatest n u m b e r of digits to th e right of any decim al point, an d th e n m ultiply by
10 raised to th a t power.``````

``````Pr o b l em 5 Solving an Equation That Contains Decimals
What is the solution of 3.5 — 0.02x = 1.24?``````

``````— - - -................................
The e q u a tio n c o n ta in s te n th s (3.5) and h u n d re d th s (0.02 a nd 1.24). The
g re a te s t n u m b e r o f d ig its to th e r ig h t o f any d e cim a l p o in t is 2. So, m u ltip ly
each side of the equation by 10 2, o r 100 , to cle a r th e decim als.``````

``````3.5 - 0.02jc= 1.24
100(3.5 - 0.02x) = 100(1.24) Multiply each side by 102, or 100.
350 - 2x = 124 Distributive Property
350 - 2x - 350 = 124 - 350 Subtract 350 fro m each side.
— 2 x= -226 Simplify.
— 2 x -226
-2 -2 Divide each side by -2.
x= 113 Simplify.``````

``Got It? 5. W hat is th e solution of 0.5x - 2.325 = 3.95? C heck your answer.``

Lesso n Ch eck

``````Do y o u k n o w H OW?

1. 7p + 8 p ~ 12 = 59 2. - 2 ( 3 x + 9) = 24
4. 1.2 = 2.4 — 0.6x

2. Gardening There is a 12-ft fence on one side of a
rectangular garden. The gardener has 44 ft of fencing
to enclose the o th er th ree sides. W hat is th e length of
the garden’s longer dim ension?

``````MATHEMAtlCAL
Do y o u UN DERSTAN D? PRACTICES
Explain how you would solve each equation
6. 1.3 + 0.5x = -3 .4 1``````

1. 7 ( 3 x - 4 ) = 49

2. 2 - 9 -x — 4 = J -* 18

3. Reasoning Ben solves th e eq u a tio n - 2 4 = 5(g + 3)
by first dividing each side by 5. Amelia solves the
eq u a tio n by using th e Distributive Property. W hose
m eth o d do you prefer? Explain.

``(-igafiagMWBaai Lesson 2-3 So l v i n g M u l t i - St e p Eq u a t i o n s L 9 7``