Solving and graphing linear inequalities is similar to the methods used for linear equations. The same rules apply for determining the slope and y‐intercept, as well as how to algebraically solve for x.
The nice thing about solving algebraic inequalities is that the process is the same as balancing algebraic equations and solving absolute value in algebraic equations.
The only difference is that whenever you multiply or divide both sides of the linear inequality by a negative number the direction of the sign switches.
Showing or graphing inequalities on a number line isn’t very different from showing a value on a number line. The only difference is that an inequality will have many solutions.
A trick to remember which way to draw the arrow is to look at the inequality sign. The direction it is pointing creates an arrow for you.
Graphing linear inequalities is similar to graphing linear equations. The same rules apply for determining the slope and y‐intercept. However, the graphs look slightly different because the lines can either be dashed or solid and include shading depending on the sign of the inequality.
The rules for graphing linear inequalities are:
Answers to Practice Problems