Solving inequalities and using interval notation as solution

Question

How would I go about solving the equation (x+3)(x+1)(x-2)>= 0 and put it in interval notation?

Answer 1

Let's solve this inequality bu using 'Snake' method.

Right side function f(x) = (x+3)(x+1)(x-2) is a product of three factors and

so it has 3 zeros: x = -3, 1, 2 (note that these values satisfy the inequality).

They divide the number line (all real numbers) into 4 intervals: (-inf, -3), (-3, 1), (1, 2), (2, inf).

On each of these intervals f(x) remains positive or negative, and it changes between positive

and negative values only when x crosses those 3 zeros.

On (2, inf) interval (where x > 2) f(x) > 0, because every factor is positive here.

On (1, 2) interval (where 1 < x < 2) f(x) < 0.

On (-3, 1) interval f(x) > 0.

On (-inf, -3) interval f(x) < 0.

Answer: x >= 2 or -3 <= x <= 1

Interval notation answer: x ∈ (-3, 1) U (2, ∞)