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What are possible values of m if l2m+3l < 12 and m is an integer?

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clara2 | Student, Undergraduate | eNoter

Posted April 5, 2011 at 12:10 PM via web

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What are possible values of m if l2m+3l < 12 and m is an integer?

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

Posted April 5, 2011 at 12:15 PM (Answer #1)

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l 2m +3 l <12

We need to find  the values of m such that m belongs to Z.

By definition we will rewrite:

==> -12 < 2m+3 < 12

 

We will subtract 3 from both sides.

==> -15 < 2m < 9

Now we will divide by 2.

 

==> -15/2 < m < 9/2

==> -7.5 < m < 4.5

Since m is an integer, then we will find all integers between -7.5 and 4.5

==> m = { -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}

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academicsfirst | High School Teacher | (Level 2) Adjunct Educator

Posted April 5, 2011 at 6:40 PM (Answer #2)

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We are asked to find integer values for |2m + 3| < 12.

This is an absolute value inequality, therefore there are two cases which must be considered.  We can write the 2 cases and solve as follows:

=> -12 < 2m +3 < 12

=> -12 -3 < 2m < 12 - 3

=> -15 < 2m < 9

=> -15/2 < m < 9/2

Therefore m is equal to integer values which are greater than    -7 1/2  but less than 4 1/2.

The solution set is { -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4 }

 

 

 

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