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Absolute Value Inequalities

A series of free Intermediate Algebra Lessons from Thinkwell's online Algebra series. Thinkwell's products and courses are being used by thousands of students at schools and universities across the globe.

Absolute Value Inequalities
To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. Absolute value inequalities can have one or two variables. Solving and graphing absolute value inequalities with two variables is also a skill that math teachers require students to master in Algebra I.

Absolute Value Inequality Graphs in Two Variables
Graphing inequalities with two variables can be tricky and is made even more tricky when we graph inequalities with two variables and absolute value. With absolute value graphing, if the inequality is similar to the equation of a line, (for example y > m|x| + b), then we get a V shape, and we shade above or below the V. This is very similar to graphing inequalities with two variables. The difference is that we are graphing inequalities with absolute values which makes the V-shape.

Shifts in Absolute Value Graphs
Once we learn about absolute value graphing, we can use shifts in absolute value graphs to more easily graph new absolute value equations. We can use specific rules for the addition of constants within the equation to shift the graph horizontally or vertically. These techniques can also be used when graphing parabolas.

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