To solve an absolute value with inequalities, you use the same steps as solving a normal absolute value problem, but with one more step.
First, start solving as if it were a normal absolute value problem.
When you get your two answers you plot them on a number line. If the sign in your problem is a "less/greater than or equal to" you shade in your plotted points. If it is just a "less/greater than" sign you leave the circle open, or unshaded. These plotted points are called "critical points".
Then you pick three numbers to test in the original equation. One number must be lesser than the lower critical point, one greater than the higher point and one that's between the two points. If a test point works, you shade from one of your critical points toward the point and all numbers included in that shading answer the inequality.
Answers are written with the "x"being compared to the two critical points using inequality signs. Here are examples: 6 < x < 9
x <>9
I don't really see the point in me posting this since all the notes are already on the blog, but here it is anyway.
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Forrest - Maybe try to think of it from the point of view of someone who wasn't in class. Your writeup provides the narrative to go along with the notes. The notes make sense to you because you were present for the explanations in the lesson. If you didn't know what you were looking at, the narrative can help explain it.
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