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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 Absolute Value 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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