Algebra 1 Common Core Student Edition, Grade 8-9

Solving Inequalities Using

Multiplication or Division

Common Core State Standards

A-CED.A.1 Create... inequalities in one variable

and use them to solve p ro b le m s... Also N-Q.A.2,

A-REI.B.3

MP 1, MP 2, MP 3, MP 4, MP 7

Ob ject i ve To use m ultiplication or division to solve inequalities

Getting Ready! X C

This pattern can

help you rem em ber

the properties

you'll learn in

this lesson.

Co n si d er t h e i n eq u al i t y 4 > 1. Co p y an d co m p l et e each

st at em en t a t t h e r i g h t b y r ep l aci n g each w i t h <

or >. W hat happens to the inequality symbol when you

multiply each side by a positive number? W hat happens

to the inequality symbol when you multiply each side by

a negat ive num ber? Ju st if y your reasoning.

4-3 • 3

4-2 •2

4- 1 • 1

4- -1 • -1

....4- ....... .-2 • -2

4- -3 • - 3

MATHEMATICAL

PRACTICES in th e Solve It, you m ay have noticed th at m ultiplying b o th sides of an inequality by a

negative n u m b e r affects th e inequality symbol.

Essential U nderstanding Just as you u sed m ultiplication a n d division to solve

eq u a tio n s in C hapter 2, you can use m ultiplication an d division to solve inequalities.

Key Concept Multiplication Property of Inequality

Words

Let a, b, and c be real num b ers

with c > 0.

If a ^•> ib, then cic be.

If a bt then ac ^ be.

Let a, b, and c be real num b ers

with c < 0.

If a > b, then ac < be.

If a < b, then ac > be.

These p roperties are also tru e for inequalities using > an d <.

178 Chapter 3 Solving Inequalities