Question

How do you solve the inequality `((2x+1)/(x-5))<=0`?

Answer 1

[-1/2, 5)

Explanation:

`f(x) = (2x + 1)/(x - 5) <= 0`
Solve this inequality by creating a sign charge (sign table) that shows the variation of of the 2 binomials, when x varies.
First solve the 2 binomials:
2x + 1 = 0 --> x = -1/2
x - 5 = 0 --> x = 5
Sign chart.
The sign of f(x) is the resultant sign of the 2 binomials.
Answer: `f(x) <= 0` in the closed interval [-1/2, 5]
The 2 endpoints (1/2) and (5) are included.