How do you solve the equation? [absolute value(6t-9)]-21=0

When you solve an equation that contains absolute value,
you'll have to consider 2 cases.

First, we'll re-write the
equation using mathematical symbol for absolute
value:

|6t-9| - 21 = 0

Now,
we'll add 21 both sides:

|6t-9| =
21

We'll factorize by 3 to the left
side:

|3(2t - 3)| = 21

3|2t -
3| = 21

We'll divide by 3:

|2t
- 3| = 7

We'll discuss 2
cases:

2t-3 for
2t-3>=0

2t>=3

t>=3/2

-2t
+ 3 for
2t-3<0

2t<3

t<3/2

Case
1: t belongs to the interval [3/2, +infinite).

2t - 3 =
7

2t = 10

t =
5

Since t = 5 belongs to the range [3/2, +infinite), we'll
accept it as solution.

Case 2: t belongs to the interval
(infinite,3/2).

-2t + 3 =
7

-2t = 4

t =
-2

Since t = -2 belongs to the range (infinite,3/2), we'll
accept it as solution.

The solutions of the
given equation are: {-2 ; 5}.