solve and check the inequalites |4m+8|<12. can you show me the calculations.

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grebjack | High School Teacher | (Level 1) Adjunct Educator

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The absolute value of 4m + 8 is either just 4m + 8 (it was already positive so the absolute value didn't change it) or it is -(4m + 8) because it was negative and the absolute value changed its sign.  So 4m + 8 < 12 and -(4m + 8) < 12.  In the second inequality, I'd like to multiply both sides by -1, but that will flip the sign of the inequality since numbers on the negative side of the number line are in the reverse order of numbers on the positive side.  That gives me 4m + 8 > -12.  I can combine these two inequalities into a single compound inequality:

-12 < 4m + 8 < 12


Now I'll subtract 8 from all three parts of the compound inequality:

-20 < 4m < 4

Then I'll divide through by a factor of 4:

-5 < m < 1

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