To graph an absolute value inequality, start by pretending like the inequality sign was an equals sign and graph the "v" shape as you would have a regular equation. Then, if the inequality is < or >, you'll need to make your "v" dashed lines. If the inequality is <= or >= , you can leave your lines as solid lines. Your last job is going to be to shade either inside or outside the "v"- the shaded region needs to represent the area of the graph where the solution, or "true" points are. Pick any test point that is not on the v and plug in those x and y values to test the inequality. If you get a true inequality, then shade where that point was- if you get a false inequality, then shade away from that test point.
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