Solve the inequality. Write the solution set in interval notation.
-$$2 x ^ { 2 } + 9 x

Question

Solve the inequality. Write the solution set in interval notation.
-$$2 x ^ { 2 } + 9 x < 35$$
A) $\left( - 7 , \frac { 5 } { 2 } \right)$
B) $\left( \infty , - \frac { 5 } { 2 } \right) \cup ( 7 , \infty )$
C) $( \infty , - 7 ) \cup \left( \frac { 5 } { 2 } , \infty \right)$
D) $\left( - \frac { 5 } { 2 } , 7 \right)$

Quizplus · Accepted Answer

First, rearrange the inequality to $2x^2 + 9x - 35 < 0$, then factor or use the quadratic formula to find the roots $x = -7$ and $x = \frac{5}{2}$. The inequality is satisfied between these roots, so the solution in interval notation is $\left( -7, \frac{5}{2} \right)$.

Solve the Inequality 2x2+9x<352 x ^ { 2 } + 9 x < 352x2+9x<35

Solve the Inequality $2 x ^ { 2 } + 9 x < 35$