What is x if 4 | 2x-6 | + 8 = 12

We'll solve the absolute value equation as it
follows:

4 | 2x-6 | + 8 =
12

We'll first subtract 8 both sides in order to isolate
the absolute value to the left side:

4 | 2x-6 |  = 12 -
8

4 | 2x-6 |   = 4

We'll
divide by 4:

| 2x-6 |  =
1

We'll get 2 cases to
solve:

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

2x-6>=0

2x>=6

x>=3

Now,
we'll solve the equation:

2x-6 =
1

We'll add 6 both sides:

2x =
7

x = 7/2 = 3.5 > 3

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

[7/2 , +inf.)

2)
2x-6<0

2x<6

x<3

Now,
we'll solve the equation:

2x-6 =
-1

We'll subtract 6 both
sides:

2x = 5

We'll divide by
2:

x = 5/2

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

Since both values of x respect the
constraints of the modulus, they represent solutions of the equation: {5/2 ;
7/2}.