Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 2 x + 7 } { x - 7 } \leq 0$$
A) $\left[ - \frac { 7 } { 2 } , 7 \right)$
B) $\left[ - \frac { 7 } { 2 } , 7 \right]$
C) $\left[ - \infty , - \frac { 7 } { 2 } \right] \cup ( 7 , \infty )$
D) $\left[ - \infty , - \frac { 7 } { 2 } \right] \cup [ 7 , \infty )$

Question

Quizplus · Accepted Answer

To solve the inequality $\frac { 2 x + 7 } { x - 7 } \leq 0$, we find the zeros of the numerator and the undefined points of the denominator. The numerator $2x + 7 = 0$ gives $x = -\frac{7}{2}$, and the denominator $x - 7 = 0$ gives $x = 7$, which is an undefined point and not included in the solution set. Testing intervals around these points shows that the inequality holds for $x \in \left[ - \frac { 7 } { 2 } , 7 \right)$.

Solve the Rational Inequality 2x+7x−7≤0\frac { 2 x + 7 } { x - 7 } \leq 0x−72x+7​≤0

Solve the Rational Inequality $\frac { 2 x + 7 } { x - 7 } \leq 0$