Solve the inequality. Write the solution set in interval notation.
-$$- 3 x ^ { 2 } + 8 x \geq 0$$
A) $\left[ 0 , \frac { 8 } { 3 } \right]$
B) $\left[ - \frac { 8 } { 3 } , 0 \right]$
C) $\left( - \infty , - \frac { 8 } { 3 } \right] \cup [ 0 , \infty )$
D) $( - \infty , 0 ] \cup \left[ \frac { 8 } { 3 } , \infty \right)$

Question

Quizplus · Accepted Answer

To solve the inequality $-3x^2 + 8x \geq 0$, factor out the common term $x$, giving $x(-3x + 8) \geq 0$. The roots are $x = 0$ and $x = \frac{8}{3}$. Testing intervals around these roots shows that the inequality holds for $x$ in the interval $\left[0, \frac{8}{3}\right]$.

Solve the Inequality −3x2+8x≥0- 3 x ^ { 2 } + 8 x \geq 0−3x2+8x≥0

Solve the Inequality $- 3 x ^ { 2 } + 8 x \geq 0$