We need to solve the equation:
|8x + 5| = 29
In order to do so, we need to consider two cases:
0. When ,8x + 5 ≥ 0.
,
1. When ,8x + 5 < 0.
For the first case, the quantity inside the symbol | ... | is already non-negative. So, its absolute, which turns the expression into a non-negative one, won't do any changes:
0. When ,8x + 5 ≥ 0:
|8x + 5| = 8x + 5
|8x + 5| = 29
8x + 5 = 29
8x + 5 - 5 = 29 - 5
8x = 24
8x/8 = 24/8
x = 3
Now, for the second case, the quantity inside the symbol | ... | is negative. So, the symbol | ... | will change the sign of the expression inside it in order to make it non-negative:
0. When ,8x + 5 < 0:
|8x + 5| = -(8x + 5)
|8x + 5| = 29
-(8x + 5) = 29
-(8x + 5) * (-1) = 29 * (-1)
8x + 5 = -29
8x + 5 - 5 = -29 - 5
8x = -34
8x/8 = -34/8
x = -4.25
Therefore, the solution is {-4.25, 3}.