3l x-2 l + 7 = 12

First let us move 7 to th left sides:

==> 3 l x-2l = 5

Now let us divide by 3 both sides:

==> l x-2 l = 5/3

Now we have two possible solutions:

case (1):

x-2 = 5/3

==> x= 5/3 + 2

==> x= (5+6)/3 = 11/3

**==> x= 11/3**

Case(2)

-(x-2) = 5/3

==> -x + 2 = 5/3

==> -x = 5/3 - 2

==> -x = (5-6)/3 = -1/3

**==> x= 1/3**

**==> x= { 1/3, 11/3}**

To solve 3|x-2|+7 = 12.

|x-2| is the positive of the expression (x-2).

So |x-2| = x-2 when x> 2. And |x-2| = 2-x , when x < 0.

Therefore when x > 2, the given equation is:

3(x-2)+7 = 12.

3(x-2) = 12-7 = 5.

x-2 = 5/3.

x = 2+5/3 = 11/3.

When x < 2, the given equation could be written as:

3(2-x)+7 = 12.

6 -3x +7 = 12

-3x+13 = 12.

-3x = 12-13 = -1.

x = -1/-3 = 1/3.

x= 1/3.

Therefore from the cases , the solution we get : x= 11/3 or x= 1/3.