Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0$$
A) $( - \infty , - 7 ) \cup ( 3,4 )$
B) $[ - 7,3 ] \cup ( 4 , \infty )$
C) $( - \infty , - 7 ] \cup [ 3,4 )$
D) $[ 3,4 )$

Question

Quizplus · Accepted Answer

To solve the inequality $\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0$, we find the zeros of the numerator and the undefined point of the denominator. The zeros of the numerator are $x = 3$ and $x = -7$, and the denominator is undefined at $x = 4$. Plotting these points on a number line and testing intervals, we find that the inequality is satisfied for $x \in ( - \infty , - 7 ]$ and $x \in [ 3,4 )$.

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Solve the Rational Inequality $\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0$