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# Module 9 - Math113

### Absolute Value Equations and Inequalities

What is |x| ? This is the distance from 0.
How many solutions are there for |x|=10 ? There are two; x=10 and x=-10.
What symbol denotes a union between to absolute value inequalities? U
What are you trying to find between two absolute value inequalities joined by the word, "and"? The intersection.
What is the first step to solving |x|+5>2 ? Isolate the AV by subtracting 5 from both sides. This means |x|>-3 and there is no solution.
If |x|< -2, how many solutions are there? None; an AV inequality cannot equal a negative number.
When "a" is positive, then |x|=a is equivalent to what? x=-a, a
What are the two forms of absolute value inequalities? |x|>a and |x|<a
How would you solve |x|>a ? Create two separate inequalities: x>a and x<-a
How would you solve |x|<a Use the form -a<|x|<a.
Created by: 1313621852