Question

What are the critical points for the inequality 2x+5/x-2≥x-1/x-2?

A. x=-5/2, x=1, and x=2
B. x=-6 and x=2
C. x=-4 and x=2
D. x=2

Answer 1

B. x=-6 and x=2

Explanation:

Which shows all the critical points for the inequality?

x = 1, and x = 2

x = –6 and x = 2

x = –4 and x = 2

x = 2

Answer 2

1) When the denominator equals zero that is a critical point

=> x - 2 = 0 => x = 2.

So x = 2 is a critical point

2) Simplify the numerator to find an expresion of the king p(x) ≥ 0 or p(x) ≤ 0. Where p(x) equals zero you have other(s) critical point(s)

Multiply both terms:

[2x + 5] / [ x - 2] = [x - 1] / [x - 2]

for x ≠ 2 => 2x + 5 = x - 1

=> 2x - x = - 1 - 5

=> x = - 6

Then, the two critical points are x = 2 and x = - 6.

Answer: option B.