Solving a question that contains only inequality, or an equation that is specifically based on equations is rather a fun math to solve but GRE is here to test your complete mathematical skills and its true they won’t be asking you straight-forward questions, they will mix these two together to confuse you. But a little practice and patience; and inequalities will be your least worried topics in GRE, in fact if your concepts are clear not even a single point will be deducted of yours.

So, what inequalities means?

In simple words if spoken, any equation without the sign of equality is known as inequality.

## Types of Inequalities

- x greater than y, x >y
- x less than y, x<y
- x less than or equal to y, x ≤ y
- x greater than or equal to y, x ≥y
- x lying in between range a1 and a2, a1 <x < a2; this is known as compound inequality.

The basic difference between an equation and an inequality is, an equation gives you the concrete result of a variable whereas an inequality only provides you with a range.

For example, consider these two equations x = 3 and x >3

The first equation gives you a single value, i.e. x= 3

While the second one is an inequality and it does not provide any specific value of x, in place it only restricts the value of x that it can’t be less than or equal to 3.

## Addition and Subtraction of Inequalities

Question: x + 4 > 16. Find x.

Solution: x + 4 > 16

x > 12

Let’s take another example:

-p + 2q > q – 2p, which of the following holds good?

- p > 0
- q > 0
- p + q > 0
- p + q <0

Solution: Lets combine these terms together:

-p + 2q > q – 2p

+2p +2p

———————–

p + 2q >q

p + 2q > q

-q > -q

p + q >0

Hence the correct option is (c).

## Multiplication and Division of Inequalities

Important Tip: If you are multiplying or dividing an inequality with a positive value then the arrow of inequality does not change but if the value to be multiplied or divided is negative then the arrow should be reversed.

For example: -6x > 12

Solution: \(\frac{-6x}{-6} > \frac{12}{-6}\)

\(x > -2\)But remember the tip given above, flip the arrow

\(x < -2\)Another point to keep in mind is you cannot divide or multiply an inequality with a variable. The reason behind this rule is that, the sign of variable is unknown so it would be incorrect to divide or multiply by a variable.

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