Question 221961
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x-2| + 10\ =\ 12]


Add -10 to both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x-2|\ =\ 2]


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 - 2 = 2\ \Rightarrow\ x = 4]


Or:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x - 2 = -2\ \Rightarrow\ x = 0]


Everyone who does it the same way will obtain the correct answer.


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