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Solving Inequalities

After studying this lesson, you will be able to:

• Solve inequalities.

The inequality symbols are:

> greater than

greater than or equal to

< less than

less than or equal to

The steps for solving inequalities are the same as those for solving equations:

1. Remove parentheses

2. Collect like terms on each side of the inequality symbol

3. Get the variables together on one side

4. Isolate the variable

5. Check

** There is one major difference in solving inequalities than equations: WHEN MULTIPLYING OR DIVIDING BY A NEGATIVE, REVERSE THE INEQUALITY SYMBOL.

Example 1

 x + 8 > 10 x + 8 - 8 > 10 - 8 Subtract 8 from each side x > 2 This is the solution

Check by substituting a number greater than 2 into the original inequality:

3 + 8 >10

11>10 it checks!

Example 2

 y - 4 6 y - 4 + 4 6 + 4 add 4 to each side y 10

Check by substituting a number less than or equal to 10 into the original inequality:

9 - 4 6

5 6

Example 3

 6x - 10 26 6x - 10 + 10 26 + 10 Add 10 to each side 6x 36 Divide each side by 6Notice we divided by positive 6 so the inequality Symbol stays the same x 6 This is the solution...check by substituting into the original inequality