Question 732940
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Add 9 to both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6|1\ -\ 5x|\ =\ 66]


Divide both sides by 6


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |1\ -\ 5x|\ =\ 11]


Apply the definition of the absolute value function:


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


So if *[tex \LARGE 1\ -\ 5x\ \geq\ 0] then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ 5x\ =\ 11]


Add -1 to both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5x\ =\ 10]


Divide both sides by -5


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


But if *[tex \LARGE 1\ -\ 5x\ <\ 0] then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ 5x\ =\ -11]


Add -1 to both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5x\ =\ -12]


Divide both sides by -5


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{12}{5}]


Hence the solution set is *[tex \LARGE \left{\frac{12}{5},\,-2\right}]


I leave it as an exercise for the student to check the answers.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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