Algebra 1 Common Core Student Edition, Grade 8-9

Goal

Solving Multi-Step

Inequa ities

Ob ject ives To solve m ulti-step inequalities

Common Core State Standards

A-REI.B.3 Solve linear equations and inequalities

in one variable, including equations w ith coefficients

represented by letters. Also A-CED.A.1

MP 1, MP 2, MP 3, MP4

1 ' ' G e t t i n g R e a d y!

Math Club members are selling Pi Day T-shirts for $7.50

each. Th e goal is t o raise $500 by Frid ay. The f igure at

the right shows how much they have raised by Wednesday.

What is the minimum number of T-shirts they must still

sel l in o r d er t o r each t h e i r g o al? Ex p l ai n y o u r r easo n i ng.

sense of th e

problem. W hat

inform ation do you

need b efo re finding

t h e minimum num ber

of T-shirts?

mathematical ^ ° u can m °d e l th e situation in th e Solve It w ith th e inequality 337.50 + 7.50x > 500. In

PRACTICES this lesson, you will learn how to write a n d solve m ulti-step inequalities like this one.

Esse n t i a l U n d e r st a n d i n g You solve a m ulti-step inequality in th e sam e way

you solve a one-step inequality. You u se th e properties of inequality to transform the

original inequality into a series of simpler, equivalent inequalities.

9 + 4f > 21

9 + 4t—9>21 — 9

pian _ ._^4 t>^12

How can you check At. 12

the solutions?^4 4

Check the endpoint, 3. t> 3

Then choose a value

greater than 3 and check Check 9 + 4(3) —^21

the inequality symbol. w

21=21

9 + 4(4) =2= 21

25 > 2 1

Using M ore Than One Step

What are the solutions of 9 + 4t > 21? Check the solutions.

S ubtract 9 fro m each side.

Simplify.

Divide each side by 4.

Simplify.

Check the endpoint of t > 3 by substituting 3 for t in the

related equation.

Simplify.

Check the in e q u a lity sym bol o f t > 3 by s u b s titu tin g 4 fo r t in the

original inequality.

Simplify.

186 Ch ap t er 3 So l v i n g I n e q u a l i t i e s