how to solve modulus inequality?

Dear Student,

$$\begin{gathered} Let us say, we have \\ \left|x\right|\le 2 \\ \Rightarrow \pm x\le 2 \\ \Rightarrow x\le 2 or -x\le 2 \\ \Rightarrow x\le 2 or x\ge -2 \\ \Rightarrow -2\le x\le 2 \\ In this way you can solve any inequality involving modulus operator. \end{gathered}$$$$\begin{gathered} Let us say, we have \\ \left|x\right|\le 2 \\ \Rightarrow \pm x\le 2 \\ \Rightarrow x\le 2 or -x\le 2 \\ \Rightarrow x\le 2 or x\ge -2 \\ \Rightarrow -2\le x\le 2 \\ In this way you can solve any inequality involving modulus operator. \end{gathered}$$

Hope this information will clear your doubts about topic.

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