Given the equation:

2+ 3 l 3x +1l = 11

First we need to isolate the absolute value.

Let us subtract 2 from both sides:

==> 3 l 3x + 1l = 11 - 2

==> 3 l 3x + 1l = 9

Now we will divide by 3.

==> l 3x + 1l = 3

Now we have two cases:

case(1) :

3x + 1 = 3

==> 3x = 2

==> x = 2/3

Case(2).

-(3x+1) = 3

==> -3x -1 = 3

==> -3x = 4

==> x = -4/3

Then the answer is:

**x = { -4/3 , 2/3}**

2 + 3 l 3x+1 l = 11. To solve for x.

We isolate |3x+4|. First, we subtract 2 from both sides:

3|3x+1| = 11-2 = 9.

3|3x+1| = 9.

We divide by 3:

|3x+1| = 9/3 = 3.

|3x+1| = 3....(1)

If 3x+1 > 0, or when x > 1/3. |3x+1| = 3x+1.

=> 3x+1 = 3

=> 3x = 3-1 = 2.

=> x = 2/3. So x = 2/3 is the solution when x > 1/3.

When 3x+1 < 0, or when x< 1/3, then |3x+1| = -(3x+1).

So the equation (1) becomes: -(3x+1) = 3

=> -3x-1 = 3.

=> -3x = 3+1 = 4.

=> x = -4/3, when x< 1/3. So x = -4/3 is the solution.

Therefore x = 2/3. Or x= -4/3.