Absolute value represents the distance from zero on a number line. Therefore to solve this absolute value equation we must represent both distances from zero.

Splittin this in to eqch equation makes the 2 equations given.

a) `8x - 3 = x + 4`

`7x = 7`

`x = 1`

b) `-(8x-3) = x + 4`

`-8x + 3 = x + 4`

`-9x = 1`

`x = -1/9`

**The solutions are `x = 1` and `x = -1/9`**

The equation | 8x - 3 | = x + 4 has to be solved.

|8x - 3| = 8x - 3 for 8x - 3 >= 0 or x >= 3/8

and |8x - 3| = 3 - 8x for 8x - 3 <0 or x < 3/8.

If x >= 3/8, the given equation is 8x - 3 = x + 4 or 7x = 7 or x = 1

If x < 3/8, the given equation is 3 - 8x = x + 4 or -1 = 9x or x = -1/9

The solution of the equation | 8x - 3 | = x + 4 is x = 1 and x = -1/9