Solving inequalities is very similar to solving equations with one exception. if we multiply or divide by a negative number, the symbol will need to flip directions. We will keep that in mind as we solve inequalities.
When multiplying or dividing by a negative number, the inequality sign switches. For example, greater than becomes less than, and less than becomes greater than.
The inequality we solve can get as complex as the linear equations we solved. We will use all the same patterns to solve these inequalities as we did for solving equations. Just remember that any time we multiply or divide by a negative the symbol switches directions (multiplying or dividing by a positive does not change the symbol!)
It is important to be careful when the inequality is written backwards as in the previous example (4 < x rather than x > 4). Often students draw their graphs the wrong way when this is the case. The inequality symbol opens to the variable, this means the variable is greater than 4. So we must shade above the 4.
Source: Adapted from "Beginning and Intermediate Algebra" by Tyler Wallace, an open source textbook available at: http://wallace.ccfaculty.org/book/book.html