SOLUTION: what is solution for a)|x|>-2 b)|x|-2=-3

Algebra ->  Absolute-value -> SOLUTION: what is solution for a)|x|>-2 b)|x|-2=-3       Log On


   

Question 109466: what is solution for
a)|x|>-2
b)|x|-2=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
abs%28x%29%3E-2 Start with the given inequality
Since the absolute value of any number is always positive, this means abs%28x%29%3E0. So this means the left side will always be greater than -2. So the solution set is . Basically x can be any number.

b)



abs%28x%29-2=-3 Start with the given equation


abs%28x%29=-1 Add 2 to both sides.


Since the expression abs%28x%29=-1 is never true (note: remember, the absolute value of any number is always positive), there are no solutions to abs%28x%29=-1

Also, notice if we graph y=abs%28x%29-2 and y=-3(just set each side equal to y and graph), we get:

graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cabs%28x%29-2%2C-3%29 Graph of y=abs%28x%29-2 (red) and y=-3(green)

and we can see that the two graphs never intersect. So there are no solutions.