if 2 + 3 l 3x+1 l = 11 what is x?

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.