Question

How do you solve the inequality: `x^2 + x - 6 < 0`?

Answer 1

Solve f(x) = x^2 + x - 6 < 0

Ans: Open interval (-3, 2)

Explanation:

First, find the two real roots (2 x-intercepts) by solving f(x) = 0
Factor pairs of (-6) --> (-2, 3). This sum is 1 = b. Then, the 2 real roots are: 2 and -3.
Use the algebraic method to solve f(x) < 0. Inside the interval (-3, 2), f(x) is negative (f(x) < 0), having the opposite sign to a = 1.
Answer by open interval (-3, 2).