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Basic Math/inequalities

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Expert: Josh - 1/4/2006


Question
Why does the inequality sign need to be reversed when both sides are divided by a negative number?

Answer
Kellie,

To make sense of this, just plug in some numbers.

Consider 1-x>5, ...[#0]
-x>4 ...[#1]
reversing sign gives
x<-4 ...[#2]

If we don't do this, would we have obtained the right solutions?
NOT reversing sign gives x>-4. So, let's select an easy number within this range, like x=0, for instance.
Putting this back into the original inequality [#0] gives 1-0>5, i.e., 1>5 which is obviously a contradiction.

So, we need to reverse the sign when multiplying or dividing both sides of an inequality with a negative number.

Cheers.

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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