Algebra 1 Tutorial
Solving an inequality
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.
Solve the inequality for x: x – 2 > 3
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
About The Author
|Experience Math And Engineering Tutor|
|I have been tutoring students in various levels of Mathematics and Engineering courses for over 10 years. Students ages range from 8-40. I recently obtained my BS in Electrical Engineering with a Minor in Mathematics from Sonoma State University. Pre-Algebra, Algebra, Geometry, Pre-Calculus/Trigo...|