# Solve for t if 3*l3t - 5l + 12 =< 27

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The inequality to be solved is 3*l3t - 5l + 12 =< 27

3*l3t - 5l + 12 =< 27

divide all the terms by 3

=> |3t - 5| + 4 =< 9

=> |3t - 5| =< 5

This gives :

(3t - 5) =< 5

=> 3t =< 10

=> t =< 10/3

and 3t - 5 >= - 5

=> 3t >= 0

=> t >= 0

**The value of t lies in [0, 10/3]**

Given the inequality:

3*l 3t -5 l + 12=< 27

First we will need to isolate the absolute value on one sides.

We will subtract 12 from both sides.

==> 3*l 3t -5 l =< 15

Now we will divide by 3.

==> l 3t -5 l =< 5

Now we will rewrite:

-5 =< 3t -5 =< 5

Now we will add 5 to all sides.

==> 0 =< 3t =< 10

Now we will divide by 3.

==> 0 =< t =< 10/3

**Then the values of t belong to the interval [ 0, 10/3 ]**