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How to rewrite inequalities using modulus notation?

How would you rewrite 1 <= X <= 2 ?
Original post by Baaah
How would you rewrite 1 <= X <= 2 ?


By making the interval symmetric around 0 first. So, by how much do you need to move the interval [1,2][1,2] so that it has 0 in the middle? Then just subtract that number from every part of the inequality 1x21 \leq x \leq 2

Afterwards, the modulus should follow easily since x<aa<x<a|x|<a \Leftrightarrow -a<x<a

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