
Hi, and welcome to this video on solving absolute value inequalities!
What is an Absolute Value Inequality?
An absolute value inequality is an inequality that has an absolute value on one side of the inequality.=
Remember, when you solve an absolute value equation, you come up with two answers. An absolute value inequality is similar, except instead of two answers, your answer will include all the numbers between the two that you found.
Solving Absolute Value Inequalities
To solve an absolute value inequality, remove the absolute value signs, and place the expression between the positive and negative values of the inequality given to you. Then, solve the problem like you would any other inequality expression, remembering to do the same thing to all three parts of the expression.
Example #1
Let’s look at an example to see what I’m talking about.
First, we remove the absolute value signs and place the expression between positive and negative 7, like this:
Then, we solve for
Now, divide by 3 to get
And that’s your answer. Notice how you still solve for two different numbers, but your answer is the range of numbers between those two.
Example #2
Let’s try another one.
First, get rid of the absolute value signs, and put the expression between -9 and 9.
Then, subtract 3 from each part.
And finally, divide by -2. But remember, when you divide by a negative, you have to flip the inequality signs.
And there’s your answer!
Example #3
I want you to try one more, but this time pause the video and try to figure it out yourself. Then, check your steps with mine.
First, remove the absolute value signs and place your expression between -15 and 15.
Then, add 10 to all 3 parts.
Divide by -5, remembering to flip your signs since you’re dividing by a negative.
And that’s all there is to it! I hope this video on solving absolute value inequalities was helpful. Thanks for watching, and happy studying!
Absolute Value Inequalities Practice Questions