Question

How do you solve `|4| x - 8| + 7= - 5| x - 8|`?

Answer 1

Assuming the intent was
`color(white)("XXX")color(blue)(4abs(x-8)+7) = color(green)(-5abs(x-8))`
`color(red)("No solution is possible")`

Explanation:

Since `abs(x-8) >= 0` (by definition of absolute value)

`4abs(x-8)>= 0 color(white)("xx")rarrcolor(white)("xx")4abs(x-8)+7 > 0`
but
`-5abs(x-8) < 0`

Therefore the two expressions can not be equal.