# Understanding Inequality In Algebra

**What Is an Inequality?**

Throughout the basic arithmetic we started learning in elementary school, it has been easy to understand what the “=” sign denotes. Simply put, it means that the information on both sides of the sign is equal to each other. This can be as simple as 2 + 2 = 4, ½ = 0.5 or even red =red and blue = blue.

When it comes to inequalities, everything suddenly gets flipped on its head. Instead of using an “=” sign, equations involving inequalities make use of the below four symbols:

* >: greater than*

* <: less than *

* ≥: greater than or equal to *

* ≤: less than or equal to *

The first two signs denote strict inequalities, as it is definite that the two sides aren’t equal. The last two signs carry with them a possibility that the two sides are, in fact, equal.

**Solving Inequalities **

Now, you may be wondering: how do you solve inequality? The good news is that solving inequality is much the same as solving a rational expression! Let us show you how with some examples below:

*Example1: 3x > 15*

To solve the above inequality, treat it as you would a rational expression. We know that if the equation was “3x = 15”,you would simply divide 15 by 3, and reach the conclusion that x = 5. The same goes for the above inequality, except that this time, x > 15 instead of x =15.

Simple? Let’s move on and take a look at an instance where you have to flip the inequality sign:

*Example2: -5y < 25 *

When you divide or multiply two sides of an inequality by a negative number, the inequality sign gets flipped. > becomes<, and vice versa. In order to isolate y in the above, you have to divide both sides by -5. Doing so will give you:

*y> 5*

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