Given the equation:

5 + l 2t -12 l = 7

We need to find the value of t .

First we will isolate the absolute values by subtracting 5 from both sides.

==> l 2t -12 l = 7-5 = 2

==> l 2t -12 l = 2

Now we have 2 cases:

Case(1): Positive values.

==> 2t -12 = 2

==> 2t = 14

==> t= 7..........(1)

Case(2): Negative values.

==> -(2t-12) = 2

==> -2t +12 = 2

==> -2t = -10

==> t = -10/-2 = 5

==> t= 5.............(2)

From (1) and (2) , we conclude that the values of t are:

**t = { 5, 7}**

We have 5 + l 2t-12 l = 7.

Using the property that | 2t - 12| can be 2t - 12 and -(2t - 12) based on its value, we get :

5 + (2t - 12) = 7

=> 5 + 2t - 12 = 7

=> 2t = 7 - 5 + 12 = 14

=> t = 14/2

=> t = 7

Here we also see that 2*7 - 12 = 2 is positive.

Next we take 5 - (2t - 12) = 7

=> 5 - 2t + 12 = 7

=> -2t + 17 = 7

=> 2t = 10

=> t = 5

Here we also see that 2*t - 12 = -2 is negative.

So both t = 5 and t = 7 are valid results.

**Therefore t = 5 and t = 7.**

To find t in 5 + l 2t-12 l = 7.

We subtract 5 from both sides:

|2t-12| = 7- 5= 2.

Thereore if 2t -12> 0, then 2t-12 = 2.

=> 2t = 2+12 = 14.

t= 14/2 = 7.

If 2t-12 < 0, then 2t-12 = -2.

=> 2t = -2+12 = 10.

=> 2t = 10.

=> t = 10/2 = 5.

Therefore the 2 solutions of the equation are x = 7, or x = 5.