Question

How do you solve `abs(8x+1)=23`?

Answer 1

Well this is an absolute value problem, so x can be both negative and positive.

Explanation:

As i stated earlier, it can be negative and positive, so you can end up with two different solutions, one negative and one positive.

First, to solve for the positive value, remove the absolute value |x| and set 8x+1=23, and solve for x using algebra:
`8x+1=23`
`8x=22`
`x=22/8`
`x=11/4`

Second, we need to solve for the second or negative solution, and to do this we do the same thing for the first one and remove the absolute value signs, but this time make everything outside of the absolute value negative to find the negative solution

`8x+1=-23`
`8x=-24`
`x=-3`