Question

True or False:

1. if [w-7]<-3, then w-7>3 (NOTE: In this case "[ ]" indicate absolute value.)

I did:
3+7<w-7<-3+7
10<w<4
So, I think it's False

2. If -4 < -2t + 6 < 10, then 2>t+6>-5

I worked the equation and got:
5>t>-2
So, I think it's False

Answer 1

1. correct
Be definition, |anything| has to be a positive result
so how can "+something" < -3 ? NO WAY!

2.
how about this:

-4 < -2t + 6 < 10
subtract -6
-10 < -2t < 4
divide by -2, must reverse signs
5 > t > -2
add 6 ---> we needed t+6 in the middle
11 > t+6 > 4
compare this to their answer of 2 > t+6 > -5
I conclude they are wrong.