Question

Solve the inequality


`(2x)/(x + 3) \leqslant 3`
The solution set is

Answer 1

`Domain:x\\eq-3\\\\(2x)/(x+3)\leq3\qquad\text{subtract 3 from both sides}\\\\(2x)/(x+3)-3\leq0\\\\(2x)/(x+3)-(3(x+3))/(x+3)\leq0\\\\(2x)/(x+3)-(3x+9)/(x+3)\leq0\\\\(2x-(3x+9))/(x+3)\leq0\\\\(2x-3x-9)/(x+3)\leq0\\\\(-x-9)/(x+3)\leq0\Rightarrow(x+3)(-x-9)\leq0\\\\x=-3,\ x=-9\\\\x\in(-\infty,\ -9]\ \cup\ (-3,\ \infty)`