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This is a very common trap.......if ab>ac, this does not imply that b>c.
here is the explanation

suppose a=1, b=3, c=2, which implies that ab>ac

in this case, b>c

however if a=-1, b=2 and c=3, which again implies that ab>ac

but in this case b is not greater than c

so it depends on the sign of the common variable on both sides. you can multiply or divide a variable on both sides of the inequality, only if you know the sign of an inequality. Remember, multiplying or dividing by a negative number changes the inequality sign.

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