Algebra 1 Common Core Student Edition, Grade 8-9

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Why multiply by the
reciprocal?
You want the coefficient
of m to be 1. The
product of a number
and its reciprocal is 1,
so multiply by the
reciprocal.

When the coefficient of the variable in an equation is a fraction, you can use the

reciprocal o f the fraction to solve the equation.

Solving Equations Using Reciprocals

What is the solution of gm = 28?

-m = 28

( | m ) = | ( 2 8 ) M ultiply each side by the reciprocal of

m = 3 5 Simplify.

^ G o t It? 5. a. What is the solution of 12 = |x? Check your answer.

b. Reasoning Are the equations m = 18 and \m = 12 equivalent?

H o w d o y o u k n o w?

How else can you

solve this problem?

You can work backward.

The toucan's length is j

the macaw's length, so

the macaw's length is |

the toucan's length. You

can multiply the length

of the toucan by

Problem 6 Using a One-Step Equation as a Model

Biology Toucans and blue-and-yellow macaws are both

tropical birds. The length of an average toucan is about two

thirds of the length of an average blue-and-yellow macaw.

Toucans are about 24 in. long. What is the length of an average

blue-and-yellow macaw?

Relate

le n g th o f

to u ca n

le n g th o f

is I o f b lu e -a n d -y e llo w

macaw

Define Let € = the length of an average

b lu e - a n d - y e llo w m a c a w.

Write

24 = §f?

2 v«> = rf§€

36 = €

M u ltip ly each side by |.

Simplify.

An average blue-and-yellow

m a c a w is 36 in. lo n g.

Check 24 = |€

2 4 = | ( 3 6 ) Substitute 36 fo r €.

2 4 = 2 4 Simplify. The solution checks.

G o t It? 6. An online DVD rental company offers gift certificates that you can use

to p u r c h a s e r e n t a l p la n s. Y o u h a v e a g if t c e r t if ic a t e f o r $3 0. T h e p la n y o u

s e le c t c o s ts $5 p e r m o n t h. H o w m a n y m o n t h s c a n y o u p u r c h a s e w it h

th e g if t c e r tific a te?

84 Chapter 2 Solving Equations