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

1 Answer
Apr 21, 2016

Answer:

[-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.