Solving inequalities

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1 The first lesson involves solving inequalities. They are very very similar to solving equations. The difference is that instead of having one answer, there are many possible answers. The answers are less than or greater than a particular number, so arrows are used to show that.

2 When trying to remember whether “<” or “>” are used, the best way is to think about the number line. Which way do numbers get greater on the number line? To the right, so “>” means “greater than”. Which way do numbers get lesser on the number line? To the left, so “<” means “less than”.

3 The last thing to learn is about the point or dot on the end of the arrow. Sometimes it is solid and sometimes it is hollow.

a. Solid points should be thought about as being at a particular spot and then going to the left or right. It is equal to that spot. In an equation, they are represented by having a line (kind of like half of an equal sign line) beneath, like < or >.

b. Hollow points should be thought of as having something missing. They represent everything right up next to that spot, but never reaching that spot. Since they are not equal to that point, they just have the < or > in an equation but not the equal line below.
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