Question

solve the
following inequation
x+3/x-2 =<2 , x is not equal to 2​

Answer 1

Step-by-step explanation:

We have,

$\frac{x + 3}{x - 2} \leqslant 2$

$\implies \: \frac{x + 3}{x - 2} - 2 \leqslant 0$

$\implies \: \frac{x + 3 - 2x + 4}{x - 2} \leqslant 0$

$\implies \: \frac{ - x + 7}{x - 2} \leqslant 0$

$\implies \: \frac{ x - 7}{x - 2} \geqslant 0$

$\implies \: x \in( - \infty ,2) \cup(7, \infty )$