Algebra 1 Common Core Student Edition, Grade 8-9

Inequalities and

_ i. ■ coefficients represented oy letters.

rheir G raphs mpi,mp2,mp3.mp4,mp 6

Common Core State Standards

Prepares for A-REI.B.3 Solve linear equations and

inequalities in one variable, including equations w ith

coefficients represented by letters.

Ob ject ive To w rite, g raph , a n d iden tify s o lu tio n s of in e q u a litie s

Getting Ready!

A s k e tc h m igh t

help.

MATHEMATICAL

PRA CTICES

By law , t h e hei g h t o f a new ly co n st r u ct ed

building in Washington, D .C., can be no

greater than the width of the adjacent

st r eet , plus 20 f t. Pennsylvania Avenue,

sh o w n a t t h e r i g h t , i s t h e w i d e st

st r eet in W ashingt on, D .C. W h at is

the maximum allowable height of a new

building? Explain your reasoning.

Lesso n

Vocabulary

solution of an

inequality

The Solve It involves com paring two q u an tities—th e height of a building an d the w idth

of the street adjacent to it. You can use a n inequality to com pare such quantities.

Essential U nderstanding An inequality is a m athem atical sen ten ce th a t uses an

inequality symbol to com pare th e values of two expressions. You can use a n u m b e r line

to visually re p resen t th e values th a t satisfy an inequality.

Tj^lpk, ^

Less than and is less

than have different

m eanings. For example,

"6 less th a n k" means

k - 6 , w h i l e "6 is less

than k" means 6 < k.

Writing Inequalities

What inequality represents the verbal expression?

0 all real numbers x less than or equal to — 7

all real less th a n or

numbers x equal to -7

X < -7

The inequality x < - 7 rep resen ts th e verbal expression.

0 6 less than a number k is greater than 13.

6 less th an is greater

a n u m b e r k than

k-6 >

13

13

The inequality k — 6 > 13 rep resen ts th e verbal expression.

164 Chapter 3 Solving Inequalities