Two Ways to Solve an Absolute Inequality with Two Absolute Values | Glass of Numbers

This may not be an SAT/ACT absolute inequality question, but it's more difficult than those seen on SAT or ACT. So, if you understand the two techniques demonstrated in this video about solving inequalities, you will become a lot better on your SAT or ACT preparation!

We are solving the inequality |x-4| greater than |x+2| in two ways:
1) Graphing
2) Testing Points

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[KTKMaths]

Simple & Clear cut Explanation. Thank you so much. May I know which writing platform you are using? Seems cool in your neat handwriting..

[jisotico]

in method 2, why didnt you test the 4 cases (+ +, + -, - +, - -), and only 2?

[Bfg..]

does this also work when an absolute value of like |x-3| is being divided by |x+3| and i like less than 2. So like would it work for |x-3|/|x+3| < 2. It might if the numbers are correct. So like move the bottom to the other side. And then do the same thing? IDK if that will work cus of the sign flipping jazz.

[Taskit]

testing points method doesnt always work?

[hotcornstudios]

Squaring both sides can be faster in some cases