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

Apr 21, 2016

[-1/2, 5)

#### Explanation:

$f \left(x\right) = \frac{2 x + 1}{x - 5} \le 0$
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: $f \left(x\right) \le 0$ in the closed interval [-1/2, 5]
The 2 endpoints (1/2) and (5) are included.