What is the solution set of x/4≤9/x?

Question

asked May 27, 2019 199k views

2 Answers

Nicholas Hart · Answer 1 · 2019-06-01T04:12:31+0000

Answer:

x≤-6 or 0<x≤6.Option D.

Explanation:

Given:

$(x)/(4) \leq (9)/(x).$

Subtract
(9)/(x) from both sides,

$(x)/(4)-(9)/(x) \leq$ 0

Simplifying by taking common denominator:

$(x^2-36)/(4x)\leq$ 0

Factoring numerator:

$((x+6)(x-6))/(4x)\leq$ 0

Computing the signs and selecting that one satisfies ≤ 0:

x≤ -6,0<x≤6.

Option D is the right answer.