Question

Halp! please
which answer is a solution to the inequality 4+|t+2|<11

t<5 and t>9
t>5 or t<-9
-5<t<9
-9<t<5

Answer 1

To solve for this subtract 4 from both sides.

|t+2|<7

 Now we know that our answer cannot be 7 or greater which means that t must be in between -9 and 5.

Since t cannot be greater than 5, the first answer doesn't make sense. The same with the second answer which leaves only the third answer.

The answer is -5 or -9

Answer 2

4+|t + 2| < 11

First, we have to subtract 4 from each sides of the problem. We should then simplify 11 - 4 to get 7.
$|t + 2| \ \textless \ 7$

Second, we can now rewrite the inequality without the absolute value. We basically have to split the inequality into two to remove the absolute value bars.
$-7 \ \textless \ t + 2 \ \textless \ 7$

Third, subtract 3 from each side, meaning the whole problem. (-7 - 2 = -9) and (7-2 = 5). 
$-9 \ \textless \ t \ \textless \ 5$

Answer: $\fbox {D) -9 \textless t \textless 5}$