help on absolute values in math.....?

Question

i don't understand my math homework on absolute values. i know it's like the easiest thing in the world but for some reason i don't understand this problem. if you could help me understand this problem that would be great! okay here it is: I10-(t+2)I > 1
thanks so much!! ~Joy

Answer 1

|10 - (t+2)| >1
|8 - t| >1 THIS CAN BE REWRITTEN AS
8-t>1 OR 8-t < -1
8>1+t OR 8<-1+t
7>t OR 9 WHICH WOULD BE ARE NUMBERS EXCEPT THE ONES BETWEEN 7 AND 9 ALSO EXCLUDING 7 AND 9.

IF THE ORIGINAL PROBLEM HAD BEEN <1 THEN WE WOULD OF USED THE WORD AND INSTEAD OF OR

Answer 2

I think you are supposed to find all the values of t for which the absolute value of 10-(t+2) is greater than 1.

So, try some numbers... when t is 0 the expression is 8
When t is 10, the espression is -2, the absolute value of which is 2. when t is 8, the expression is 0, so we know t= 8 is not part of the answer, because 0 is NOT greater than 1., When t is 9, the epression is -1, the absolute value of which is 1. 1 is NOT greater than 1..so 9 is not in the answer. you should also check negative values of t...It looks to me like -12 is a value that is NOT in the answer...