#### Answer

(-2,-4/3)

#### Work Step by Step

1.) Set what the inequality equals to what it originally equals, and then set it to the opposite of that number with the opposite inequality sign
3x+5$\lt$1 and 3x+5$\gt$-1
2.) Solve the first inequality for x by subtracting 5 and dividing by 3 to both sides
3x+5$\lt$1
-5 -5
3x$\lt$-4
$\div$3 $\div$3
x$\lt$-4/3
3.) Solve the second inequality for x subtracting 5 and dividing by 3 to both sides
3x+5$\gt$-1
-5 -5
3x$\gt$-6
$\div$3 $\div$3
x$\gt$-2
4.) Combine the two inequalities to get a set of values that x can equal
(-2,-4/3)