The solution set of the inequation, $3(5-x)≥\frac{x}{7}+8, x\in R $ is:

$\left(-∞, \frac{49}{22}\right]$

The correct answer is Option (3) → $\left(-∞, \frac{49}{22}\right]$

$3(5-x)≥\frac{x}{7}+8$

$⇒15-3x≥\frac{x}{7}+8$

$⇒105-21x≥7\left(\frac{x}{7}+8\right)$

$⇒105-21x≥x+56$

$⇒105-56≥x+21x$

$⇒\frac{49}{22}≥x$

$∴x∈\left(-∞, \frac{49}{22}\right]$