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Properties of inequalities/solving inequalities and equation

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Topic 1: Properties of Inequalities

We have two variables A and X.
The value of X is less than the value of A
Discuss without using any specific numbers, how we can prove that the value of ( -X) is greater than the value of( -A).

Do not use any numerical examples.

Keep in mind that A or X could be any numerical value.

Keep in mind that A or X could be a negative value.
There are two completely different ways to prove the result.
Discuss the possibilities. You need not get it exactly right the first time.

Topic 2: solving inequalities and equations

What rule of operations that applies when you are solving an equation does not apply when you are solving an inequality? Show with examples.Discuss what rules use to solve them. What is differences between an equations and inequality.

NOTE: This is a discussion about the differences in the process of solving an equation and an inequality.

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Solution Summary

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1. The best way to prove that -X is greater than -A when X<A is using a number line.

We know that if X < A, then X is nearer to zero and A is farther, both to the right side of the origin (zero).

The farther the number to zero to the right, the greater the value. The opposite is if the number is farther to the left of zero, then it has lesser value.

If we now consider the negative values of X and A, -X is nearer to zero and -A is farther, ...

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