Algebra 1 Common Core Student Edition, Grade 8-9

^ G o t It? 1. W hat is an inequality th a t re p resen ts the verbal expression?

a. all real n u m b ers p greater th a n or equal to 1.5

b. The sum of t an d 7 is less th a n - 3.

A solution o f an inequality is any n u m b e r th a t m akes th e inequality true. The solutions

of th e inequality x < 5 are all real n u m b ers x th a t are less th a n 5. You can evaluate an

expression to d eterm in e w h e th e r a value is a solution of an inequality.

Problem 2

Think
Is - 1 th e only
solution to the
inequality?
No. Any number tha t
makes the original
inequality true is a
solution o f the inequality.
The solu tio n - 1 is one
o f an infinite number o f
solutions.

Id en tifyin g Solutions b y E valuating

Is the number a solution of 2x + 1 > — 3?

Q -3 0-1

2 x + 1 > —3

2(—3) + U - 3

• 6 + 1 A - 3
  -5 > -3

■ S u b s t i t u t e f o r x.

<— Simplify. —>

Compare. —»

• 3 does n o t m ake th e original
  inequality true, so - 3 is not
  a solution.

2x + 1 > - 3

2(—1) + 1 i -3

-2 + 1 A - 3

-1 > -3

— 1 does m ake th e original

inequality true, so -1 is

a solution.

G o t It? 2. a. C onsider th e n u m b e rs —1, 0,1, an d 3. W hich are solutions of

13 - 7y < 6?

b. Reasoning In P roblem 2, how is th e solution of th e related equation

2x + 1 = - 3 related to th e solutions of th e inequality?

You can use a graph to indicate all of th e solutions of an inequality.

Inequalit y Graph

n < 1

a>0

/> -3

-2 > x

« I I.

-4 -3

.I.....

1

H b H 1 - I I-

-4 -3 -2 -1

H 1 -----I— — H

-2 -1

-5 -4 -3 -2-1 0 1

You can also w rite - 2 SxasxS -2.

H h

q— i— i— h

■+-*»

The open d o t shows th a t 1 is not a solution.

Shade to the left o f 1.

The closed d o t show s th a t 0 is a solution.

Shade to th e rig h t o f 0.

The open d o t shows th a t - 3 is not a solution.

Shade to the right o f - 3.

The closed d o t show s th a t - 2 is a solution.

Shade to the left o f - 2.

c

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