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How do i solve for this absolute value equation ? |12x - 5| = 11

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Hello, we know that


|x|=\begin{cases}x &amp;\text{if } x \geq 0\\ -x &amp;\text{if } x < 0 \end{cases}

And we can write that 12x-5=0 <=> 12x =5 <=> x = 5/12

So,


|12x-5|=\begin{cases}12x-5 &amp;\text{if } x \geq (5)/(12)\\\\ -12x+5 &amp;\text{if } x < (5)/(12)\end{cases}

And, we can write.


|12x-5|=11<=>\begin{cases}12x-5=11 &amp;\text{if } x \geq (5)/(12)\\\\ -12x+5=11 &amp;\text{if } x < (5)/(12)\end{cases}\\ \\ \\ <=>\begin{cases}12x=16 &amp;\text{if } x \geq (5)/(12)\\\\ 12x=5-11 &amp;\text{if } x < (5)/(12)\end{cases}\\\\<=>\begin{cases}x=(16)/(12)=\boxed{(4)/(3)} &amp;\text{if } x \geq (5)/(12)\\\\ x=(-6)/(12)=\boxed{-(1)/(2)} &amp;\text{if } x < (5)/(12)\end{cases}

So the two solutions are 4/3 and -1/2.

Thank you.

User Tagyoureit
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