Solve the inequality. Write the solution set in interval notation.
-$$4 x ^ { 2 } - 5 x \geq 9$$
A) $\left[ - 1 , \frac { 9 } { 4 } \right]$
B) $\left( - 1 , \frac { 9 } { 4 } \right)$
C) $( - \infty , - 1 ] \cup \left[ \frac { 9 } { 4 } , \infty \right)$
D) $( - \infty , - 1 ) \cup \left( \frac { 9 } { 4 } , \infty \right)$

Question

Quizplus · Accepted Answer

First, rearrange the inequality to standard form: $4x^2 - 5x - 9 \geq 0$. Factoring or using the quadratic formula, we find the roots to be $x = -1$ and $x = \frac{9}{4}$. Since it's a "greater than or equal to" inequality and the leading coefficient is positive (indicating a parabola opening upwards), the solution set includes values outside the interval between the roots, hence $( - \infty , - 1 ] \cup \left[ \frac { 9 } { 4 } , \infty \right)$.

Solve the Inequality 4x2−5x≥94 x ^ { 2 } - 5 x \geq 94x2−5x≥9

Solve the Inequality $4 x ^ { 2 } - 5 x \geq 9$