Solve the inequality. Write the solution set in interval notation.
-$$3 x ^ { 2 } + 14 x

Question

Solve the inequality. Write the solution set in interval notation.
-$$3 x ^ { 2 } + 14 x < 24$$
A) $\left( -\infty , - \frac { 4 } { 3 } \right) \cup ( 6 , \infty )$
B) $\left( - 6 , \frac { 4 } { 3 } \right)$
C) $ \left( - \frac { 4 } { 3 } , 6 \right)$
D) $( -\infty , - 6 ) \cup \left( \frac { 4 } { 3 } , \infty \right)$

Quizplus · Accepted Answer

First, rearrange the inequality to $3x^2 + 14x - 24 < 0$. Factoring or using the quadratic formula, we find the roots to be $x = -6$ and $x = \frac{4}{3}$. The inequality is satisfied between these roots, so the solution set in interval notation is $\left( - 6 , \frac { 4 } { 3 } \right)$.

Solve the Inequality 3x2+14x<243 x ^ { 2 } + 14 x < 243x2+14x<24

Solve the Inequality $3 x ^ { 2 } + 14 x < 24$