Question

What graph represents the solution for x^2+x-12>0

Answer 1

Answer: the solution to the inequality is -3 < x < 4. Graphically, this should be (2)

Step-by-step explanation:Note that x^2 - x - 12 factors to (x - 4)(x + 3) < 0, so we have:

(x - 4)(x + 3) < 0.The only way for (x - 4)(x + 3) to be negative is if x - 4 and x + 3 have opposite signs. This only occurs when:

(i) x - 4 < 0 AND x + 3 > 0  

==> x < 4 AND x > -3; both occur when -3 < x < 4.

(ii) x - 4 > 0 and x + 3 < 0, which cannot happen at the same time.