As I am preparing the Algebra 1 students for their math midterm exam, I was asked by a student how to solve the absolute value inequality equation. Algebra 1 students will be asked to solve inequality equations such as |3x + 6| > 9. The first thing that the students should remember is that absolute value equations (whether it be inequality or not) always has 2 solutions. The second thing that the students should remember is that the 2 solutions are not the positive and negative of a certain number.
When attempting to find the first solution for the absolute value inequality equation, students should solve it as though the absolute value is not present. In our example, we should solve the inequality of 3x + 6 > 9.
3x + 6 > 9
3x > 3
x > 1
So the first solution for this inequality is x > 1. Students MUST be made aware that the second solution is not taking the first solution and making the number negative (for example x > -1). The correct way to solve the absolute value inequality equation is to make sure that the absolute value term is on one side of the inequality and just negate the other side of the inequality equation while also switching the inequality. In our example, the absolute value is standing alone on the left side of the inequality, so we will just negate the right hand side while also switching the inequality.
|3x + 6| > 9
3x + 6 < -9
3x < -15
x < -5
The solutions for the inequality of |3x + 6| > 9 is x > 1 or x < -5. In my next blog post, I will expand on these type of absolute value equation questions, please stay tune.
If you have any question regarding this type of problems, please feel free to reach out to me or any of the instructors in my center.
Michael Huang
Mathnasium of Glen Rock/Ridgewood
236 Rock Road
Glen Rock, NJ 07452
glenrock@mathnasium.com
Tel: 201-444-8020
