The Four Signs

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

An inequality with an unknown in it, like x + 3 < 8, is a question: which numbers can x 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 them, and the answer is written as a simpler inequality: x < 5.

The moves you know from equations work here too. x + 3 < 8 is solved by subtracting 3 from both sides, exactly as x + 3 = 8 would be:

x + 3 - 3 < 8 - 3

x < 5

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