Question

How do you solve `absx - 4 =3x`?

Answer 1

There are two possible solutions, depending on whether `x` is positive or not.

Explanation:

`x>=0`
Then the equation turns into:
`x-4=3x->-4=2x->x=-2`
This in contrary to the `x>=0` condition, so this solution has to be discarded.

`x<0`
The sign for x is reversed, and the equation becomes:
`-x-4=3x->-4=4x->x=-1`
And this is acceptable.
Check: `|-1|-4=3*(-1)->1-4=-3`

Conclusion:
The only solution: `x=-1`