SOLUTION: Solve and check the inequality, if possible. |4m + 8| < 12

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Question 986111: Solve and check the inequality, if possible.
|4m + 8| < 12

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve and check the inequality, if possible.
|4m + 8| < 12
----------
|m + 2| < 3
---------
m + 2 < 3
m < 1 Solution 1
===============
-m-2 < 3
-m < 5
0 < m+5
-5 < m
m > -5 Solution 2
===============


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
abs%284m+%2B+8%29+%3C+12...............since abs%284m+%2B+8%29=sqrt%28%284m+%2B+8%29%5E2%29, we will have
4m+%2B+8%3C+12 and -%284m+%2B+8%29%3C+12
solutions:
4m+%2B+8%3C+12=>4m+%3C+12-8=>4m+%3C+4=>highlight%28m+%3C+1%29
and
-%284m+%2B+8%29%3C+12=>-4m+-+8%3C+12=>-12+-+8%3C+4m=>-20%3C+4m
=>-20%2F4%3C+m=>-5%3C+m or highlight%28m%3E-5%29
interval: -5%3Cm%3C1
so,solution set is: -4, -3,-2,-1,and 0
check:
m=-4
abs%284%28-4%29+%2B+8%29+%3C+12
abs%28-16+%2B+8%29+%3C+12
abs%28-8%29+%3C+12
8+%3C+12.............true
m=-3
abs%284%28-3%29+%2B+8%29+%3C+12
abs%28-12+%2B+8%29+%3C+12
abs%28-4%29+%3C+12
4+%3C+12.............true
m=-2
abs%284%28-2%29+%2B+8%29+%3C+12
abs%28-8+%2B+8%29+%3C+12
abs%280%29+%3C+12
0+%3C+12.............true
m=-1
abs%284%28-1%29+%2B+8%29+%3C+12
abs%28-4+%2B+8%29+%3C+12
abs%284%29+%3C+12
4+%3C+12.............true
m=0
abs%284%280%29+%2B+8%29+%3C+12
abs%280+%2B+8%29+%3C+12
abs%288%29+%3C+12
8+%3C+12.............true
number_line%28+600%2C+-10%2C+10%2C+-5%2C+1+%29