What are the values of M if  l 2m -5 l < 12  ( m is a positive integer).

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

l 2m - 5 l < 12

First we will solve the inequality the same way we solve the equations.

We have two cases.

Case(1):

(2m - 5) < 12

==> 2m < 17

==> m < 17/ 2

==> m < 8.5

==> m = ( -inf, 8.5)

But m = positive integer.

Then, m = { 1, 2, 3, 4, 5, 6, 7, 8 }

 

Case(2):

-(2m-5) < 12

==> -2m + 5 < 12

==> -2m < 7

==> m > -7/2

==> m = ( -7/2, inf)   which is impossible because m is a positive integer.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve for |2m-5|<12.

For 2m-5> 5 or m> 5/2 , |2m-5| <12 implies 2m-5 < 12.

So for m > 5/2 = 2.5,

2m-5 = 12.

2m = 12+5

m = 17/2 = 8.5.

m 8.5.

When m < 5/2 = 2.5 

|2m-5| = 5-2m.

Therefore the inequality becomes:

5-2m = 12.

5 =  12+2m.

5-12 = 2m

-7 = 2m.

-7/2 =  m.

-3.5 = m

Therefore m = -3.5.

Therefore the solutions of the inequality are x = -3.5 and x = 8.5.

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