Answer:
The solution set consists of all the real numbers smaller than or equal to 11/4:
[tex]x\leq \frac{11}{4}[/tex]
Step-by-step explanation:
We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:
[tex]3+\frac{x-2}{x-3} \leq 0\\\frac{x-2}{x-3} \leq -3\\x-2\leq -3\,(x-3)\\x-2\leq -3x+9\\x+3x\leq 9+2\\4x\leq 11\\x\leq \frac{11}{4}[/tex]
