6th Grade Math Textbook, Fundamentals

 &KDSWHU

14-10
Multiplication and Division:

Inequalities with Rational Numbers

Objective To solve one- and two-step inequalities involving rational numbers using the

Multiplication and Division Properties of Inequality • To graph the solution sets of inequalities

involving rational numbers

The giraffe at the local zoo is at least twice as

tall as the zoo’s African elephant. The elephant

is 1.85 meters taller than the zoo’s wildebeest.

If the giraffe is 6 meters tall, how tall is the wildebeest?

To find the wildebeest’s height, write and solve

an inequality.

Leth the wildebeest’s height.

Giraffe’s is at Elephant’s

height least two times height

6 2•(h 1.85)

Multiplication inequalities with rational numbers

can be solved the same way as inequalities

with integers.

Solve: 6 2(h 1.85)

6 2 h3.7 Apply the Distributive Property.

6 3.7 2 h 3.7 3.7

2.3 2 h Simplify.

Divide both sides by 2 to isolateh.

1. 15 h Simplify.

Graph:

Check: Try h1. 15. Tr yh 0.85.

6 2(1. 151.85) Substitute 1.15 forh. 6 2(0.851.85) Substitute 0.85 forh.

6 2(3) Simplify. 6 2(2.7) Simplify.

6 6 Tr u e 6 5.4 Tr u e

The zoo’s wildebeest is no more than 1.15 meters tall.

Subtract 3.7 from

both sides.

?

?

?

?

2 h

2

2.3

2

Remember:

Multiplication Property of Inequality

For any real numbers a, b, and c, where

cis positive, if a b, then ac bc.

For any real numbers a, b, and c, where

cis negative, if a b, then ac bc.

Division Property of Inequality

For any real numbers a, b, and c, where

cis positive, if a b, then a cb c.

For any real numbers a, b, and c, where

cis negative, if a b, then a c b c.

Similar statements can be written for

a b, a b, and a bfor both properties.

0.8 0.9 1.0 1.1 1.2