How do you do absolute value equations with inequalities?

So if you have an absolute value equation like $\left | 5+x \right | >7-2x$ how do you go about solving it.

I know how to solve absolute value equations with an equals sign but not with inequalities.

Thanks in advance.


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Erdos Erdos
  • Where did you the get 5+x ≥ 0 or x ≥ -5 part from?

    • Erdos Erdos

      You add -5 to both sides of the inequality.

  • Erdos Erdos

    You can do pretty much everything with inequalities that you do with equalities. The only difference is that whenever you multiply or divide both sides by a negative number, the direction of the inequality switches.

  • Thanks for the reply what I meant is why do you put a zero on the other side of the inequality? Where does the zero come from.

    • Erdos Erdos

      This comes from the basic fact about absolute values: (i) If A >= 0 then |A|=A (ii) If A<0, then |A|=-A. This is why in general we consider two cases A>=0 and A<0. In this example A=5+x.

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