# Find all t values if 3l 2t-5l =< 12

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### 2 Answers

The inequality we have is 3*|2t - 5| =< 12

3*|2t - 5| =< 12

=> |2t - 5| =< 4

We get 2 inequalities because of the absolute value

-4 =< 2t - 5

=> 1 =< 2t

=> 1/2 =< t

2t - 5 =< 4

=> 2t =< 9

=> t =< 9/2

**The values of t lie in the set [ 1/2 , 9/2]**

Given the inequality:

3*l 2t-5 l =< 12

To solve, we will need to isolate the absolute value on the left sides.

We will divide by 3.

==> l 2t-5 l =< 12/3

==> l 2t-5 l =< 4

Now by definition we can rewrite:

-4 =< 2t-5 =< 4

Now we will add 5 to all sides.

==> 1 =< 2t =< 9

Now we will divide by 2.

==> 1/2 =< t =< 9/2

**Then the values of t belongs to the interval [ 0.5 , 4.5]**