Answer:
Option (4)
Step-by-step explanation:
Given inequality is,
[tex]\frac{x}{4}\leq \frac{9}{x}[/tex]
[tex]\frac{x}{4}-\frac{9}{x}\leq 0[/tex]
[tex]\frac{x^{2}-36}{4x}\leq 0[/tex]
x ≥ 0 [For x = 0, fraction is not defined]
(x - 6)(x + 6) ≤ 0
x - 6 ≤ 0
x ≤ 6
Or
x + 6 ≤ 0
x ≤ -6
Therefore, solution set is (-∞, -6] ∪ (0, 6]
By plotting the solution area on a number line,
Option (4) will be the answer.
