Solving an inequality

Algebra 1 Tutorial

Solving an inequality

Intro

In this tutorial, I will explain how you can solve an inequality to identify the possible x values that make this inequality true. I will then describe what the actual answer means to us.

Sample Problem

Solve the inequality for x: x – 2 > 3

Solution

Our goal is to solve for x in the inequality. So this means that we must get x on one side of the inequality sign all by itself.

We see that 2 is being subtracted from x on the left side. So we ask ourselves what is the opposite of subtracting 2 from x?

Well, the answer is adding 2 to x. But we have to remember that whatever we do to one side of the inequality, we must do to the other side. So we perform this operation yielding:

x – 2 + 2 > 3 + 2

Which simplified to be:

x > 5

We have just isolated the x variable on the left side of the inequality symbol. Mission accomplished!

Now, let’s interpret what this solution means. It tells us that x must be greater than 5. Not greater than or equal to 5, but greater than 5. So this tells us that we can insert any number which is greater than 5 into the given inequality to obtain a true statement. Let’s try plugging in x = 6 into the given inequality:

6 – 2 > 3

4 > 3

Well 4 is certainly greater than 3. So this is true! Now let’s try a value that is not in the solution. For example, x = 2. Keep in mind that 2 is not greater than 5, so this should give us an untrue statement when we plug it in:

2 – 2 > 3

0 > 3

See how this statement is untrue? Because the number that we plugged in is not inside the interval x > 5



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