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Graphing inequality (Tomato subjective 90)

Problem: Draw the region of points \({\displaystyle{(x,y)}}\) in the plane, which satisfy \({\displaystyle{|y| {\le} |x| {\le} 1}}\).

Solution: \({\displaystyle{|y| {\le} |x| {\le} 1}}\) region will bounded by lines \({\displaystyle{x = y}}\), \({\displaystyle{x = -y}}\), \({\displaystyle{x = -1}}\) & \({\displaystyle{x = 1}}\). Why is that?

First note that \( |x| \le 1 \) implies:

Inequality region

 

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