Algebra 1 Common Core Student Edition, Grade 8-9

T o s o lv e a n e q u a t io n , y o u m u s t isolate t h e v a r ia b le. Y o u d o t h is b y g e t t in g th e v a r ia b le

w i t h a c o e f f ic ie n t o f 1 alone on one side of the equation.

P»ar»
How can you visualize
the equation?
You can draw a diagram.
Use a m odel like th e one
below to help you
visualize an equation. A
model for the equation
x -H 13 = 2 7 is
t 27 ..............t
I x I 13 I

Y o u c a n is o la te a v a r ia b le u s in g t h e p r o p e r t ie s o f e q u a lit y a n d in v e r s e o p e r a t io n s. A n

inverse operation undoes another operation. For example, subtraction is the inverse

of addition. W hen you solve an equation, each inverse operation you perform should

p r o d u c e a s im p le r e q u iv a le n t e q u a tio n.

Solving an Equation Using Subtraction

What is the solution of x + 13 = 27?

Jh ip R—.

You need to iso la te x. S ta rt by

writing the equation.

Undo addition by subtracting the

sam e n u m b e r fro m each side.

x + 13 = 27

x + 13 - 13 = 27 - 13

Simplify each side of the equation. x = 14

Substitute your answer into the

original equation to check it. X + 13 — 2 7

14 + 13 ^ 2 7

27 = 27

G o t It? 1. a. What is the solution of y + 2 = — 6? C h e c k y o u r a n s w e r.

b. Reasoning I n P r o b le m 1, w h y d o e s s u b t r a c t in g 13 f r o m b o t h s id e s o f th e

o r ig in a l e q u a t io n r e s u lt i n a n e q u iv a le n t e q u a tio n?

Plao
How can you get
started?
Undo operations. Add
3 to each side to undo
subtraction.

Pr o b l em 2 Solving an Equation Using Addition

What is the solution of — 7 = b — 3?

-7 = 6 -3

-7 + 3 = 6 ~ 3 + 3 Add 3 to each side.

-4 = 6 Simplify.

& G o t It? 2. What is the solution of each equation? Check your answer.

a.m-8 = -14 b.^ = y-|

82 Ch ap t er 2 So l v i n g Eq u a t i o n s