# Solving Inequalities

To solve an inequality you must get x alone on one side of
the inequality symbol with a constant on

the other side of the symbol . To get x alone in an inequality you use the same
steps as you used in

solving equations but there is **one added condition .** If you ever **
multiply or divide ** both sides of

the inequality **by a negative number ** you must **switch the direction of
the inequality symbol .**

**Solve a one step inequality by getting
the variable x alone on one side of the inequality sign **

Eliminate the constant term on the x side or eliminate the
coefficient with the x term.

1. Eliminate the constant term on the x side of the equation by adding or
subtracting the constant from

both sides of the inequality.

2. Eliminate the coefficient by multiplying or dividing both sides of the
inequality by the coefficient. **If**

**you ever multiply or divide both sides of the inequality by a negative number
then you
must switch the direction of the inequality symbol.
Examples of solving a one step inequality:**

Example 1 |
Example 2 |
Example 3 |

add +6 to both sides | divide both sides by –2 (switch the symbol) |
multiply both sides by –4 (switch the symbol) |

Example 4 |
Example 5 |
Example 6 |

subtract 5 from both sides | divide both sides by 4 | multiply both sides by 3 |

**Solving Inequalities
Solve an inequality by getting the variable x
alone on one side of the inequality sign **

Get the variable x alone using the same steps as you did in solving equations in Chapter 6.

1. Distribute and combine like terms on each side of the equal sign.

2. Get the x term on only one side of the equation by
adding or subtracting the smallest x term from

both sides of the inequality.

3. Eliminate the constant term on the x side of the
equation by adding or subtracting that constant from

both sides of the inequality.

5. Eliminate the coefficient by multiplying or dividing
both sides of the inequality by the coefficient. **If**

**you ever multiply or divide both sides of the inequality by a negative number
then you
must switch the direction of the inequality symbol.**

Example 1 |
Example 2 |
Example 3 |
Example 4 |

Example 5 |
Example 6 |
Example 7 |
Example 8 |

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