Understanding Inequality In Algebra

One of the basic algebraic concepts students have to grasp is inequality. It can sound simple but once you get down to solving equations, understanding what an inequality means can become more challenging. In this handy guide, we help you understand what inequality in algebra means and share with you some examples.

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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