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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.

Evaluating Expressions

         

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

If \(-12 \leq a < 12\), what is the value of \[ \lvert a-14 \rvert + \lvert a-12 \rvert + \lvert a+12 \rvert + \lvert a+14 \rvert ?\]

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

When \(-19\leq x\leq y\leq4,\) which of the following is equivalent to \[\lvert x+19\rvert+\lvert x-y\rvert+\lvert y-4\rvert?\]

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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