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# Basic Algebra

# Solving Inequalities

**Solving inequalities** is not that much different than solving equations. Instead of having an equal sign divide the two sides, there is an inequality sign.

However, there is one really important rule:

**if you multiply or divide by a negative number you have to flip the inequality sign.**

For example, let's look at .

solve like you would -2x + 3 = 5 | |

subtract three from each side | |

simplify | |

divide each side by -2 | |

switch the sign from > to < |

With this last example, if we had divided by positive two instead of negative two, we would have found that –x > 1. So, x < -1 and –x > 1 are really the same thing! That's why we have to switch the sign when we divide or multiply by a negative.

Since we divided by a -2, we switched the sign from > to <. Now, just like equations we can check our answers. Since x < -1, to check pick any number less than -1 and plug it into the original inequality (we picked -2).

Well 7 *is* greater than 5 so we can be pretty confident that we solved this correctly. However, unlike equations, we can't be completely sure. If you want to double check your work, that wouldn't be a horrible idea.

**Look Out:** only switch the inequality sign if you multiply or divide by a negative number. You do not switch it if you add or subtract a negative number.

Did you forget what inequalities were and became confused by this section? Well, here's a helpful refresher!