Algebra 1 Common Core Student Edition, Grade 8-9

How can you find
the solution of an
equation?
You can use m e n ta l
m ath to fin d a va lu e th a t
makes the equation true.

How can you start?
You can use m e n ta l m ath
to quickly check values
like 0 ,1 , and 10. Use
these results to choose a
reasonable starting value
fo r y o u r table.

Can iden tifyin g a

pattern help you

make an estimate?

Yes. Identify h o w the value

of the expression changes

as you substitute fo r the

variable. Use th e pattern

you fin d to w o rk tow a rd

the desired value.

Pr o b l em 4 Using M ental M ath to Find Solutions

What is the solution of each equation? Use mental math.

Think

0 x + 8 = 12 W h a t n u m b e r p lu s 8 equals 12?

Solution

4

72

Check

4 + 8 = 12

0 1 = 9 W h a t n u m b e r d iv id e d b y 8 e q u a ls 9?

G o t It? 4. W h a t is th e s o lu t io n o f 12 — y = 3? Use m e n ta l m ath.

72

8 9

Using a Table to Find a Solution

What is the solution of 5n + 8 = 48? Use a table.

Make a table of values. Choose a starting value using mental math. 5(1) + 8 = 13 and

5(10) + 8 = 58, so 1 is too low and 10 is too high.

Tr y n = 5

and n = 6. H

5n + 8

Value of "

5n + 8

5 5(5) + 8 33

65(6) + 8 38

7 5(7) + 8 43

(^8) 5(8) + 8 48
The val u e of 5n + 8
increases as n increases, so
try greater values of n.
When n = 8, 5n + 8 = 48.
So t h e s o l u t i o n i s 8.
Got It? 5. a. W h a t is th e s o lu t io n o f 2 5 - 3p = 55? Use a table.
b. W h a t is a g o o d s t a r t in g v a lu e to s o lv e p a r t (a )? E x p la in y o u r re a s o n in g.
Estimating a Solution
What is an estimate of the solution of — 9x — 5 = 28? Use a table.
To estim ate the solution, fin d the integer values o f x betw een w h ich the solution m ust
lie. - 9 ( 0 ) - 5 = - 5 a n d - 9 ( 1 ) - 5 = - 1 4. I f y o u t r y g r e a te r v a lu e s o f x , th e v a lu e o f
—9 x - 5 g e ts f a r t h e r f r o m 28.
Try lesser values,
su ch a s x = - 1
and x = -2.
■ -9x —^5
Kj j f nj vn
BSCS
-1 —9 ( - 1 ) - 5 4
-2 9( 2) -^513
-3 —9(—3) - 5^22
-4 —9 ( —4 ) - 5 31
Now the values of - 9 x - 5
ar e get t i ng cl oser t o 28.
28 is bet ween 22 and 31,
so t h e so l u t i o n i s b et w een
-3 and -4.
G ot It? 6. What is the solution of 3x + 3 = — 22? U s e a ta b le.
[ L e s s o n 1 - 8 An Introduction to Equations
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