Solve the inequality. Write the solution set in interval notation.
-$3 x ^ { 2 } + 7 x

Question

Solve the inequality. Write the solution set in interval notation.
-$3 x ^ { 2 } + 7 x < 20$
A) $\left( - 4 , \frac { 5 } { 3 } \right)$
B) $( - \infty , - 4 ) \cup \left( \frac { 5 } { 3 } , \infty \right)$
C) $\left( - \frac { 5 } { 3 } , 4 \right)$
D) $\left( - \infty , - \frac { 5 } { 3 } \right) \cup ( 4 , \infty )$

Quizplus · Accepted Answer

First, rearrange the inequality to $3x^2 + 7x - 20 < 0$. Factoring or using the quadratic formula gives roots at $x = -4$ and $x = \frac{5}{3}$. Since it's a "less than" inequality and the coefficient of $x^2$ is positive (implying a parabola that opens upwards), the solution set is between the roots, hence $(-4, \frac{5}{3})$.

Solve the Inequality 3x2+7x<203 x ^ { 2 } + 7 x < 203x2+7x<20

Solve the Inequality $3 x ^ { 2 } + 7 x < 20$