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Solving and Graphing Inequalities

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Inequalities are useful for finding a range of solutions. Solving and graphing inequalities is a key to finding and showing that range. We can solve inequalities using a lot of the same methods as those in solving multi-step equations when dealing with additive inverses, although some things are different when solving inequalities using multiplication. We graph inequalities using number lines.

There's a few things you want to remember when you're asked to solve and graph inequalities with only one variable, one variable meaning one letter. It might show up in more than one time in the inequality statement but there's only one letter that's the difference here. Okay first thing to keep in mind is that you're going to solve it as if there was an equal sign, use your solving techniques where you do the same thing to both sides. Whatever you're doing to one expression or one side of the inequality sign you have to do the exact same thing to the other, whether it's adding something or dividing by something or whatever it has to be the same.

The next thing is that if you're graphing on a number line you're going to want to use open circles and closed circles. Open circle is every time your inequality statement had one of these signs greater than or less than. You're going to use a closed circle if it's greater than and equal to or less than or equal to. There's one other trick that we're going to get to when it comes to multiplying or dividing with inequalities and that's sometimes you need to change the direction of the inequality. I'm just going to say this now and this may or may not make sense to you were you are in your Math class, but hear what it is. If ever when you're solving you multiply or divide by a negative number with an inequality the inequality is going to change direction, and you'll see a lot of that when it comes to doing some examples.