Answer
(-3,1)
Work Step by Step
1.) Solve the inequality equation for 0
$x^{2}$ + 2x $\lt$3
-3 -3
$x^{2}$ + 2x -3 $\lt$0
2.) Factor the inequality
(x-1)(x+3) $\lt$0
3.) Test numbers because the equation uses $\lt$0 we know we want our x-values to be negative:
--Testing 0: ((0)-1)((0)+3) $\lt$0 = -3$\lt$0
--Testing -4:((-4)-1)((-4)+3) $\lt$0 =5$\lt$0
--Testing 2: ((2)-1)((2)+3) $\lt$0 =5$\lt$0
4.) Using this information we know the x interval is (-3,1) because that is when the values tested negative.
Answer: (-3,1)
