Use the quadratic formula or graphing methods to
-$$9 x ^ { 2 } \leq 3 - 3 x$$
A) $x \leq \frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768$ or $x \geq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$
B) $x \leq \frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768$
C) $\frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768 \leq x \leq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$
D) $x \geq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$

Question

Quizplus · Accepted Answer

First, rearrange the inequality to standard form: $9x^2 + 3x - 3 \leq 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 9$, $b = 3$, and $c = -3$, we find the roots. The inequality is satisfied between these roots, leading to the correct interval $\frac{-1 - \sqrt{13}}{6} \leq x \leq \frac{-1 + \sqrt{13}}{6}$.

Use the Quadratic Formula or Graphing Methods to - 9x2≤3−3x9 x ^ { 2 } \leq 3 - 3 x9x2≤3−3x

Use the Quadratic Formula or Graphing Methods to
- $9 x ^ { 2 } \leq 3 - 3 x$