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

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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}**

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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