Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1

Tm nki^^
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