Question

solve for x.
$x^2 - x - 12 < 0$
write the solution using interval notation. use the union symbol ∪ to express the solution as a union of disjoint intervals. finite endpoints of all intervals should be integers. if there are no solutions, use the symbol ∅ for the empty set. use the set notation {a} to represent an isolated solution a.

Explanation:

Step1: Factor the quadratic expression

$x^2 - x - 12 = (x-4)(x+3)$

Step2: Find critical points

Set $(x-4)(x+3)=0$, so $x=4$ and $x=-3$.

Step3: Test intervals for inequality

Test $x<-3$: $(-)(-)=+>0$ (not valid)
Test $-3Test $x>4$: $(+)(+)=+>0$ (not valid)

Step4: Write in interval notation

Use open intervals since inequality is strict.

Answer:

$(-3, 4)$