Algebra 1 Common Core Student Edition, Grade 8-9

A solution of an equation c o n t a in in g a v a r ia b le is a v a lu e o f th e v a r ia b le t h a t m a k e s

th e e q u a t io n t r u e.

How can you tell if a

number is a solution

of an equation?

Substitute the number

for the variable in the

equation. Simplify each

side to see if you get a

true statement.

Elan ____
Why do you need
to test each answer
choice?
You should test each
answer choice in case
you made a calculation
error. If you get two
correct answers, then
you know you need to
double-check your work.

Pr o b l em 2 Id en tifyin g Solutions o f a n Equation

Is x = 6 a solution of the equation 32 = 2x + 12?

32 = 2x + 12

3 2 = 2 ( 6 ) + 12 Substitute 6 fo rx.

32 =h 2 4 Simplify.

No, x = 6 is n o t a s o lu tio n o f th e e q u a tio n 32 = 2x + 12.

G o t It? 2. Is m = ^ a solution of the equation 6 m — 8 = —5?

In real-w orld problem s, the w ord is can indicate equality. You can

represent som e re a l-w o rld situations using an equation.

Writing an Equation

Multiple Choice An art student wants to make a

model of the Mayan Great Ball Court in Chichen

Itza, Mexico. The length of the court is 2.4 times its

width. The length of the student’s model is 54 in.

What should the width of the model be?

C£> 2.4 in.

CD 11-25 in.

Relate

Define Let

Write 54

The

le n g th

w

CD 22.5 in.

CD 129.6 in.

is 2 .4 t im e s th e w id t h

= th e w i d t h o f th e m o d e l.

=2.4 • w

Test each answ er choice in the equation to see if it

is a s o lu tio n.

Satellite v ie w o f Chichen Itza

C heck A:

54 = 2Aw

54 3= 2.4(2.4)

54 * 5.76

The correct answer is C.

Check B:

54 = 2.4 w

54 — 2.4(11.25)

54 ¥= 27

Check C:

54 = 2.4w

54 = 2.4(22.5)

54 = 54

Check D:

54 = 2Aw

54 ± 2.4(129.6)

54 ± 311.04

& G o t It? 3. T h e le n g t h o f th e b a ll c o u r t a t L a V e n ta is 14 t im e s th e h e ig h t o f its w a lls.

W r it e a n e q u a t io n t h a t c a n b e u s e d t o f i n d th e h e ig h t o f a m o d e l t h a t h a s a

le n g th o f 49 cm.

54 Ch ap t er 1 Fo u n d a t i o n s f o r A l g e b r a