For what values of t does the inequality hold? 5-3l 2t-3l < -16

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We have to solve the inequality 5 - 3*l2t-3l < -16

5 - 3*l2t - 3l < -16

=> - 3*l2t - 3l < -16 - 5

=> - 3*l2t - 3l < -21

=> 3*l2t - 3l > 21

=> l2t - 3l > 7

=> 2t - 3...

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We have to solve the inequality 5 - 3*l2t-3l < -16

5 - 3*l2t - 3l < -16

=> - 3*l2t - 3l < -16 - 5

=> - 3*l2t - 3l < -21

=> 3*l2t - 3l > 21

=> l2t - 3l > 7

=> 2t - 3 > 7 and 2t - 3 < -7

=>  2t > 10 and 2t < -4

=> t > 5 and t < -2

Therefore t should be greater than 5 or less than -2.

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Given the inequality:

 5 - 3 l 2t -3 l < -16

First, we will solve the way we solve any equation.

We need to isolate the absolute values on the left side.

Let us subtract 5 from both sides.

==> -3 l 2t -3 l < -16-5

==> -3 l 2t -3 l < -21

Now we will divide by -3 and reverse the inequality.

==> l 2t -3 l > -21/-3

==> l 2t -3 l > 7

Now we have two cases:

Case(1):

(2t -3 ) > 7

==> 2t > 10

==> t > 5

==> t = (5, inf)..............(1)

Case(2):

-(2t-3) > 7

==> -2t +3 > 7

==> -2t > 4

==> t < -2

==> t= (-inf, -2)............(2)

From (1) and (2) we conclude that:

t= (-inf, -2) U (5, inf)

OR:

t= R- [ -2, 5]

Approved by eNotes Editorial Team