Question

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

Answer 1

Hello, we know that

`|x|=\begin{cases}x &\text{if } x \geq 0\\ -x &\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 &\text{if } x \geq (5)/(12)\\\\ -12x+5 &\text{if } x < (5)/(12)\end{cases}`

And, we can write.

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

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

Thank you.