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# Absolute Value

Absolute value is a mathematician's way of judging numbers by their magnitude rather than their positive/negative value. It is the distance of the number from 0 on a number line.

If \(15<x<39\), what is the value of \[|x-15|+|x-39|?\]

If \(9 \leq a < 29\), what is the value of \[|a-9|+\sqrt{(a-29)^2}?\]

If \(-6\leq x\leq-4,\) what is the value of \[\lvert2x+12\rvert+\lvert x+4\rvert+\lvert x-1\rvert?\]

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