Question

solve: x-1/2x-1> x-3/2x-5

Answer 1

Question 32969

One needs to solve $\frac{x - 1}{2x - 1} > \frac{x - 3}{2x - 5}$ .

Moving right part of inequality to the left, $\frac{x - 1}{2x - 1} - \frac{x - 3}{2x - 5} > 0$ , from which

$\frac{(x - 1)(2x - 5) - (x - 3)(2x - 1)}{(2x - 1)(2x - 5)} > 0$ . Opening brackets in the nominator, obtain

$\frac{2}{(2x - 1)(2x - 5)} > 0$ .

Roots of denominator are $x = 0.5$ ; $x = 2.5$ . Finding the signs of $\frac{2}{(2x - 1)(2x - 5)}$ on intervals $(-\infty, 0.5)$ ; $(-0.5, 2.5)$ ; $(2.5; \infty)$ , obtain $+ - +$ . Hence, the solution is $x \in (-\infty, 0.5) \cup (2.5, \infty)$ .