Question

Solve the rational inequality (x-3)/(x+4)>=0. A) x≤−4 or x>3

B) x<−4 or x≥3
C) x≤−4 or −4D) x<−4 or −4≤x≤3

Answer 1

To solve the rational inequality (x-3)/(x+4)>=0, we need to find the values of x that satisfy the inequality. The solution is x ≤ -4 or x > 3.

Step-by-step explanation:

To solve the rational inequality (x-3)/(x+4)>=0, we need to find the values of x that satisfy the inequality. We can do this by examining the sign of the numerator and the sign of the denominator.

1. If the numerator (x-3) is positive and the denominator (x+4) is positive, or if the numerator is negative and the denominator is negative, then the inequality is satisfied.

2. If the numerator is positive and the denominator is negative, or if the numerator is negative and the denominator is positive, then the inequality is not satisfied.

By using these conditions, we can determine that the solution to the inequality is x ≤ -4 or x > 3.