Question

What is the solution of 3+ x-2/x-3 less than or equal to 0

Answer 1

The solution set consists of all the real numbers smaller than or equal to 11/4:

`x\leq (11)/(4)`

Explanation:

We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:

`3+(x-2)/(x-3) \leq 0\\(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 (11)/(4)`