6th Grade Math Textbook, Fundamentals

 &KDSWHU

3-4

Update your skills. See page 409 VI.

Solve Inequalities Using Addition

and Subtraction

Objective To solve one-step inequalities by applying the Addition and Subtraction Properties

of Inequality • To graph the solution set of an inequality

Eddie’s little brother has been saving only dollar bills
in a piggy bank. On Monday, after he put $12 into his
piggy bank, there was at least $33 in it. How much money
was in Eddie’s little brother’s piggy bank before Monday?

To find how much money, write and solve an inequality.

Let y the dollars in the piggy bank before Monday.

dollars before Monday plus dollars added is at least $33

y  12 33

Solve inequalities involving addition the same way

you solve addition equations.

Solve: y 12 33

y 12  1233  12

y 21 Simplify.

Since only dollar bills were put into the bank, the solution set

is the whole numbers that are greater than or equal to 21.

Check: According to the solution set, 21 is a solution and 18 is not.

21 12 33 Substitute 21 for y. 18 12 33 Substitute 18 for y.

3333 Tr u e 3033 False

So, before Monday, Eddie’s little brother had $21 or more

in his piggy bank.

You can also solve inequalities involving subtraction

using the Addition Property of Inequality.

Solve: n 9  11

n 9  9  11  9

n 20 Simplify.

So the solution set is numbers that are less than 20.

Check: According to the solution set, 19 is a solution and 20 is not.

19 9 11 Substitute 19 for n. 20 9 11 Substitute 20 for n.

10  11 Tr u e 11  11 False

?



?



Add 9 to both sides

to isolate n.

??

Subtract 12 from both sides

to isolate y.

Think

Will the solution set to this inequality include integers,

fractions, and decimals or will it be limited to a particular

group of numbers such as whole numbers?

Key Concept

Subtraction Property of Inequality

When you subtract the same number

from both sides of an inequality,

you get a true statement.

If ab, then acbc.

This statement is also true if

is replaced by , , or.

Key Concept

Addition Property of Inequality

When you add the same number to

both sides of an inequality, you get

a true statement.

If ab, then acbc.

This statement is also true if

is replaced by , , or.