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Module 9- A. Values
Absolute Value Equations and inequalities
Question | Answer |
---|---|
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. |