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Module 9- A. Values

Absolute Value Equations and inequalities

What symbol denotes a union between two absolute value inequalities? U
What are you trying to find between two absolute value ineualites joined by thr word "and"? Intersection
What are you trying to find between two absolute value inequalites joined by the word "or"? Union
What is the first step when solving: (av)5y-1(av)-7=4 Isolate the absolute value by adding 7 to both sides.
When a is positive, then (av)x(av)=a is equivalent to: x=a, or x=-a
When a is positive, then (av)x(av) -a < x < a
When a is positive, then (av)x(av)>a is equal to: x<-a or x>a
Without having to solve, which form would the answer to this inequality be in? (av)x-3(av)>7 Either: (-8,20) or (-infinity, -8) U (20, infinity) (-infinity, -8) U (20, infinity) Because this inequality is in the form (av)x(av)>a
Why does the solution for (av)x(av)>a require two solution sets? Because absolute value means "distance from zero," "greater than" can be a number either to the right or left of the zero. This can require to sets of numbers.
Created by: icanreed