Solving Inequalities: An Overview (page 1 of 3)

Solving linear inequalities is very similar to solving linear equations , except for one small but important detail: you flip the inequality sign whenever you multiply or divide the inequality by a negative. The easiest way to show this is with some examples:

Graphically, the solution is:

Note that the solution to a less than, but not equal to inequality is graphed with a parentheses (or else an open dot) at the endpoint, indicating that the endpoint is not included within the solution.

Graphically, the solution is:

Note that x in the solution does not have to be on the left. However, it is often easier to picture what the solution means with the variable on the left. Don’t be afraid to rearrange things to suit your taste.

Graphically, the solution is:

Note that the solution to a less than or equal to inequality is graphed with a square bracket (or else a closed dot) at the endpoint, indicating that the endpoint is included within the solution.

Graphically, the solution is: