Question 500713
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Let *[tex \Large u\ =\ |x|]


Then substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8u\ -\ 10\ =\ 4u\ +\ 8]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4u\ =\ 18]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u\ =\ 4.5]


Then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x|\ =\ 4.5]


Apply the definition of absolute value:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x|\ =\ \left\{\ \ x\text{ if }x\ \geq\ 0\cr-x\text{ if }x\ <\ \,0\right]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 4.5]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -4.5]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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