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Solving One-Step Linear Inequalities

Inequalities are mathematical sentences comparing two quantities that are not equal (or possibly not equal). There are five inequality symbols:

x 3 x is not equal to 3
x < 3 x is less than 3
x > 3 x is greater than 3
x 3 x is less than or equal to 3
x 3 x is greater than or equal to 3

Some linear inequalities can be solved with a single operation. For this type of inequality, use the inverse operation to solve.

Example 1:

Solve for n .

n + 8 < 10

The inverse operation of addition is subtraction. So, subtract 8 from both sides.

n + 8 8 < 10 8 n < 2


Example 2:

Solve for y .

3 y 15

The inverse operation of multiplication is division. So, divide both sides by 3 .

IMPORTANT: Whenever you multiply or divide both sides of an inequality by a negative number, reverse the inequality.

3 y 3 15 3 y 5

When you're done solving an inequality, you may be asked to graph it. See the lesson on Graphing Linear Inequalities if you need help.


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