Question

Need help... Fast! will give brainiest What is the solution set of x/4 < 9/x ?

Answer 1

Answer:

Option (4)

Step-by-step explanation:

Given inequality is,

$\frac{x}{4}\leq \frac{9}{x}$

$\frac{x}{4}-\frac{9}{x}\leq 0$

$\frac{x^{2}-36}{4x}\leq 0$

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.