The Four Signs

An equation says that two things are equal. An inequality says that one thing is smaller or larger than the other. There are four inequality signs: < means less than, > means greater than, ≤ means less than or equal to, and ≥ means greater than or equal to. The open side of the sign always faces the larger number, so 3 < 7 and 7 > 3 say the same thing.

An inequality with an unknown in it, like x + 3 < 8, asks which numbers x can be. Here x can be 4, or 2, or 0, or -100, or 4.9. It cannot be 5 or anything larger. Instead of one answer, there is a whole range of answers. You write the answer as a simpler inequality: x < 5.

The steps you know from equations work for inequalities too. To solve x + 3 < 8, subtract 3 from both sides, the same way you would solve x + 3 = 8:

x + 3 - 3 < 8 - 3

x < 5

Every number below 5 makes the original inequality true. No number at or above 5 does.