## Related questions with answers

Question

What are all the values for $x$ such that $x^2<3 x+18 ?$ (A) $x<-3$ (B) $-3<x<6$ (C) $x>-3$ (D) $x<6$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 6To find the solution for the inequality, manipulate the inequality so that the other side is equal to $0$.

$\begin{aligned} x^2&<3x+18\\ x^2-(3x+18)&< 3x+18-(3x+18)\color{#4257b2}{\text{\quad Subtract $3x+18$ from each side.}}\\ x^2-3x-18&<0\color{#4257b2}{\text{\qquad\qquad\qquad\qquad~~~ Simplify.}} \end{aligned}$

Factor the quadratic expression.

$\begin{aligned} (x-6)(x+3)&<0 \end{aligned}$

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