3 l 5x-3 l + 8 = 11 solve for XI think I wrote the question correctly :)

We'll solve the module in ths
way:

3 l 5x-3 l + 8 =
11   

We'll subtract 8 both sides
first :

3 l 5x-3 l = 11-8

3 l
5x-3 l = 3

We'll divide by
3:

 l 5x-3 l = 1

We'll get 2
cases to solve:

1) We'll impose the constraint of absolute
value:

5x - 3 for 5x -
3>=0

5x>=3

x>=3/5

Now,
we'll solve the equation:

5x - 3 =
1

We'll add 3 both sides:

5x =
4

x = 4/5

The value of x
belongs to the interval of admissible values:

[3/5 ,
+inf.)

2) -5x + 3 for 5x -
3<0

5x<3

x<3/5

Now,
we'll solve the equation:

-5x + 3 =
1

We'll subtract 3 both
sides:

-5x = -2

We'll divide
by -5:

x = 2/5

Since the value
of x belongs to the interval of admissible values, x = 2/5 is also a root of the given
equation.

The roots of the equation are: {2/5
; 4/5}.