6th Grade Math Textbook, Fundamentals

 &KDSWHU

3-6

Update your skills. See page 411 XI.

Solve Inequalities Using Division

Objective To solve one-step inequalities by applying the Division Property of Inequality

• To graph the solution set of an inequality

Ben found some whole shells on the beach.
Emma found three times as many whole shells
as Ben. Emma found at least 15 whole shells.
How many whole shells did Ben find?

To find how many whole shells Ben found, write and

solve an inequality.

Let ythe number of whole shells Ben found.

3 times the number is greater than

that Ben found or equal to 15

3 y 15

Solve inequalities involving multiplication the

same way you solve multiplication equations.

Solve: 3 y 15

Simplify.

y 5

So the solution set is the whole numbers greater than or equal to 5.

Check:According to the solution set, 10 is a solution and 4 is not.

3(10) 15 Substitute 10 for y. 3(4) 15 Substitute 4 for y.

30  15 Tr u e 12  15 False

So Ben found 5 or more whole shells.

When an inequality is divided by a negative number,

the symbol must be reversed to form a true statement.

Solve: 6  2 b

6 (2)  2 b(2)

 3 b Simplify.

The solution set is the numbers greater than or equal to 3.

Check: According to the solution set, 3 is a solution and 10 is not.

6 2(3) Substitute 3 for b. 6 2(10) Substitute 10 for b.

6 6 Tr u e 6 20 False

15

3

5

1

3

3

1

1

y

15

3

3 y

3

?

?

? ?

Divide both sides by 2 to

isolate band reverse the

inequality symbol.

Divide both sides by 3 to isolate y.

Key Concept

Division Property of Inequality

(divide by a positive number)

When you divide both sides of an

inequality by the same positive

number, you get a true statement.

If aband cis positive, then .

A similar statement can be written for

ab, a b, and a b.

b

c

a

c

Key Concept

Division Property of Inequality

(divide by a negative number)

When you divide both sides of an

inequality by the same negative

number andyou reverse the inequality

symbol, you get a true statement.

If aband cis negative, then .

A similar statement can be written for

ab, a b, and a b.

b

c

a

c