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Question 370142: 3(7 - m) < 4(2 - m)
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! 3(7 - m( < 4(2 - m)
Solving inequalities is nearly exactly the same as solving equations. (The only exception is: If you multiply or divide both sides of an inequality by any negative number, then the inequality symbol must be reversed.)
First we simplify each side:
21 - 3m < 8 - 4m
Second we get the variable on just one side. To avoid having to remember the exception I described above, it is helpful to gather the variable terms on the side with the larger coefficient. Since -3 is larger than -4, I am going to get the variable on the left side (where the -3m is) by adding 4m to each side:
21 + m < 8
Last of all we isolate the variable. In this equation we want the 21 to go away. So we'll subtract 21 from each side:
m < -13
which is the solution.
If we don't end up with a positive coefficient for the variable, then the last step will be to multiply or divide each side by a negative number. For example, with your problem, after we simplify
21 - 3m < 8 - 4m
we could get the variable on just one side by adding 3m to each side:
21 < 8 - m
Then subtract 8 from each side:
13 < -m
And last of all we divide both sides by -1 (which means we need to remember the exception):
-13 > m
(Note how the inequality symbol has been reversed!) This solution is the same as the one we found earlier. They both say "m is less than -13". (Always read inequalities from where the variable is. So for "-13 > m" we should read it from right to left because the variable in on the right. And from right to left "-13 > m" says "m is less than -13".)
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