Question

How do you solve the absolute value equation `x+absx=28`?

Answer 1

If `x<0`, the `abs(x)=-x` and `x+absx = 0 !=28` so we must have `x>0` and `absx = x` so we need `x+x=28` and `x=14`

Answer 2

Answer is `x = 14`

To solve this equation you need to understand what `|x|`
means.
The Magnitude of `x` (denoted `|x|)` simply means the positive side of a number(`x`)

If `x` is positive or `0` (`x>=0`) then `|x| = x`
and if `x` is negative (`x<0`) it imples `|x| = -x`

Example:
`|5| = 5` because `5` is already positive
`|-11| = -(-11)` because `-11` is negative

Back to our question:
`x + |x| = 28`

There will be at most two values of `x`, because there are two possibilities; either `x >=0` or `x<0`

Case 1: `x>=0`
`=> x + x = 28`

`=> 2x = 28 => x = 14`

Case 2: `x<0`
`=> x - x = 28 => 0 = 28`
but we know that `0!= 28` So the above(last) statement is inconclusive

So the only value we can retain is `x = 14`