Solving Multi-Step Absolute-Value Inequalities
Solve multi-step absolute value inequalities in Grade 9 algebra. Isolate the absolute value, split into two compound inequalities, and graph solution sets on a number line.
Key Concepts
New Concept The expression $|c 29.75|$ represents the difference between the actual circumference and 29.75 inches.
What’s next Next, you'll use this idea to solve multi step inequalities and apply it to problems like defining acceptable product specifications.
Common Questions
How do you solve a multi-step absolute value inequality?
First isolate the absolute value expression using inverse operations, then split into two inequalities: positive case and negative case (flipping the inequality sign for the negative).
When does an absolute value inequality use AND vs. OR?
|x| < a gives a compound AND inequality (-a < x < a). |x| > a gives a compound OR inequality (x < -a or x > a).
How do you graph the solution of an absolute value inequality?
Plot boundary points on a number line with open or closed circles, then shade the appropriate region based on the inequality direction.