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 answer. I'm not sure where I went wrong?

Guest Sep 14, 2014

#1**+10 **

|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 !!)......

CPhill
Sep 14, 2014

#1**+10 **

Best Answer

|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 !!)......

CPhill
Sep 14, 2014