The question in my trig homework reads, |2t+5|< 3 I get the answer -1>t>-1 but my answer key to check my answers says this is the wrong answ

|2t+5|< 3

To solve this kind of problem, let's take the expression out of the absolute value bars and solve two equations:

2t + 5 < 3         and   -(2t + 5) < 3

The reason for this is that if,   lal < b,  then  l-al is also < b........!!!!

Working with the frist one, we have....

2t < -2      divide by 2 on each side

t < -1

Working with the second one, we have

-2t - 5 < 3   add 5 to both sides

-2t < 8        divide by -2 on both sides and reverse the sign

t > -4

So the solution is given by

-4 < t < -1

Here's a graph here  ...  https://www.desmos.com/calculator/q7apmwkdop

( I've substitued "x" for "t" but it's the same idea !!)......