Question

[y+4]<1

Answer 1

If |x|<1, then we are looking for all the numbers that have a distance of less than 1 from 0.
Those are the numbers between -1 and 1. All of these numbers that are in that set from -1 to 1 is a solution to |x|<1. You would say -1<x<1.

So if we have |f(x)|<1=> -1<f(x)<1
Solve for x.


If we had |x|>1, then we say we want all the numbers outside the interval from -1 to 1 because these numbers all have distances greater than 1 from 0.

So you would say x>1 or x<-1

Of if you had |f(x)|>1=> f(x)>1 or f(x)<-1

Now watch out for when you have |f(x)|< negative.
This won't happen |f(x)| will be positive or zero output. You will not have negative output.
There would be no solution to |f(x)|<negative

If we had |f(x)|>negative, well the solution would be all x where f is defined because |f| would be positive or zero which is always to the right of the negatives.

Answer 2

so out of these options the answer would be
-5<y<-3 correct answer
-3<y<5
-4<y<1
-<y<4

Answer 3

yep that is right.

Answer 4

thanks

Answer 5

np