Question 247802
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Use the definition of absolute value:


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


Since you don't know whether *[tex \LARGE x\ -\ 5] is positive or negative, you have to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x\ -\ 5|\ =\ \left\{\ \ x\ -\ 5\ \text{ if }x\ -\ 5\ \geq\ 0\cr-(x\ -\ 5)\ \text{ if }x\ -\ 5\ \ <\ \,0\right]


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 5\ =\ 4]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 5\ =\ -4]


The solution set is the union of the solution sets of the two equations.  *[tex \LARGE 1] is one element of your solution set, but there is another element as well.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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