Michael J. answered • 02/02/16
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Applying SImple Math to Everyday Life Activities
Solve the inequality for x.
-11x < 55
Divide both sides of the inequality by -11. Be sure to flip the comparison sign.
x > 5
Pick any 3 values that is greater than 5. Those are your solutions.
Michael J.
We flip the signs when dividing both sides of an inequality by a negative number because we must obey how the signs behave when multiplying and dividing numbers.
2 negatives yield a positive.
2 positives yield a positive.
1 positive and 1 negative yield a negative.
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02/02/16
Sriniwas T.
Thanks for throwing more light on why we should flip the sign when we have "ineqaulity".
assume both side are negative ( no need to change) when we multiply or divide by -1
-A<-B => -1x-A<-B x-1 =>A<B (NO FLIP HAPPENS)
both side are positive number
A<B => -1 * A < -1*B=>-A <-B (NO FLIP HAPPENS)
-A< B=> -1*-A < -1 * B=> A>B(FLIP HAPPENS i.e., no -ve sign to B=>-B)
Sorry if i misunderstood... Please correct me If I am wrong
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02/02/16
Michael J.
Lets take your statement: -A < -B
You have negatives on both sides of the inequality. By logic,
A > B
Let A=2 and B=1
Then plugging in these values into the statement results in
-2 < -1 ---> true statement
Now lets solve for A from the inequality to prove the logic.
-A < -B
Divide both sides of the inequality by -1. Also, we flip the sign.
A > B
This matches the logic I mentioned earlier.
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02/02/16
Sriniwas T.
Wow Excellent way to explain.....easy to understand.. Your explanation is wonderful....Lot of thanks to you
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02/02/16
Sriniwas T.
way to think about it. Multiplying a quantity by -1 changes it into
its opposite. For example, 3 becomes the opposite of 3 or -3, and 12
becomes the opposite of 12, which is -12.
Now think about how these numbers fall on a number line:
----------------------0----1----2----3--------------------12-----
Since 3 < 12, three is closer to zero and twelve is farther away.
That's true in general. Numbers with larger magnitudes are farther
away from zero.
Now what happens if we take opposites? That is, if we multiply or
divide these numbers by -1? Opposites are the same distance from zero
so -12 will be farther away from 0 than -3:
--- -12 --------------- -3 ----- 0 ---------------------------
This is true in general. If A < B and both are positive, then the
opposite of B will be farther to the left than the opposite of A, that
is, -B < -A which means the same thing as -A > -B. If you just look at
the symbols it seems as if we put minus signs in front of each letter
and switch the inequality symbol. But if you look at the meaning of
the symbols on the number line it is much clearer:
-B -A 0 A B
---------------------------------------------------------
If you look at a number line picture for A < B where both numbers are
negative instead of positive (for example -4 < -1) you will see the
same pattern occurs when you take the opposite of each.
The final case is A < B where A is negative and B is positive. You can
draw a number line picture for this case too, but it is almost simpler
to just think about the meaning of the opposites. If A is negative,
then its opposite, -A, is a positive number. If B is positive, then its
opposite, -B, is a negative number. Of course, any negative number is
smaller than any positive number so -B < -A.
02/02/16