Absolute Value

Evaluating Absolute Value Expressions


If 15<x<3915<x<39, what is the value of x15+x39?|x-15|+|x-39|?

If 12a<12-12 \leq a < 12, what is the value of a14+a12+a+12+a+14? \lvert a-14 \rvert + \lvert a-12 \rvert + \lvert a+12 \rvert + \lvert a+14 \rvert ?

If 9a<299 \leq a < 29, what is the value of a9+(a29)2?|a-9|+\sqrt{(a-29)^2}?

When 19xy4,-19\leq x\leq y\leq4, which of the following is equivalent to x+19+xy+y4?\lvert x+19\rvert+\lvert x-y\rvert+\lvert y-4\rvert?

If 6x4,-6\leq x\leq-4, what is the value of 2x+12+x+4+x1?\lvert2x+12\rvert+\lvert x+4\rvert+\lvert x-1\rvert?


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