Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 2 x } { - 5 x + 9 } \geq 13$$
A) $\left[ \frac { 117 } { 67 } , \frac { 9 } { 5 } \right)$
B) $\left[ 0 , \frac { 9 } { 5 } \right)$
C) $\left( - \infty , \frac { 117 } { 67 } \right] \cup \left[ \frac { 117 } { 67 } , \infty \right)$
D) $( - \infty , 0 ] \cup \left( \frac { 9 } { 5 } , \infty \right)$

Question

Quizplus · Accepted Answer

The inequality is equivalent to $2x \geq 13(-5x + 9)$, which simplifies to $2x \geq -65x + 117$. Subtracting $2x$ from both sides gives $-67x \geq 117$, and dividing both sides by $-67$ (reversing the inequality because $-67$ is negative) gives $x \leq \frac { 117 } { 67 } $. The solution set is therefore $\left[ \frac { 117 } { 67 } , \frac { 9 } { 5 } \right)$.

Solve the Rational Inequality 2x−5x+9≥13\frac { 2 x } { - 5 x + 9 } \geq 13−5x+92x​≥13

Solve the Rational Inequality $\frac { 2 x } { - 5 x + 9 } \geq 13$