Algebra 1 Common Core Student Edition, Grade 8-9

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?

Solve each equation. Check your answer.

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

7. 7 ( 3 x - 4 ) = 49


8. 2 - 9 -x — 4 = J -* 18


9. 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