Given the equation:

l 5x + 8 l = 17

We have the absolute value of (5x+8).

Then, we have two cases:

Case(1):

(5x + 8) = 17

Now we will subtract 8 from both sides.

==> 5x = 17 - 8

==> 5x = 9

Now we will divide by 5.

==> x = 9/5

Case(1):

-(5x+8) = 17

==> -5x - 8 = 17

Now we will add 8 to both sides:

==> -5x = 17+8

==> -5x = 25

Now we will divide by -5.

==> x = -5.

Then the answer is:

**x = { -5, 9/5}**

We have to find x given |5x + 8| = 17

Now |5x + 8|, can have an absolute value of 17 for 5x + 8 =17 and 5x + 8 = -17.

5x + 8 =17

=> 5x = 17-8

=> 5x = 9

=> x = 9/5

5x + 8 = -17

=> 5x = -25

=> x = -25/5

=> x = -5

**Therefore x can have two values -5 and 9/5.**

To solve |5x+8|=1.

If 5x+8 > 0, then |5x+8|=1 would mean 5x+8 = 17.

So 5x = 17-8 = 9.

5x/5 = 9/5 = 1.8.

So x = 1.8 is the solution.

If 5x+8 < 0, then |5x+8| = 17 would mean -(5x+8) = 17.

Multiply both sides of -(5x+8) = 17 by -1 and we get:

5x+8 = -17.

5x = -17-8 = -25.

5x/5 = -25/5 = -5.

x = -5 is the solution.

So there are 2 solutions: x= 1.8, or x= -5.

We recall that the absolute value means:

|p| = a>0

We'll have to solve 2 cases:

1) 5x+8 = 17

We'll subtract 8 both sides:

5x = 17 - 8

5x = 9

We'll divide by 5:

x = 9/5

2) 5x+8 = -17

We'll subtract 8 both sides, to isolate x to the left side:

5x = -8 - 17

5x = -25

We'll divide by 5:

x = -5

**The equation has 2 solutions : {-5 ; 9/5}.**