Solve, without using a calculator, $\frac{x-1}{1-2x}\le 1$. Hence, solve $\frac{\left| x \right|-1}{

Question

Solve, without using a calculator, $\frac{x-1}{1-2x}\le 1$. Hence, solve $\frac{\left| x \right|-1}{1-2\left| x \right|}\le 1$ $\frac{\ln x-1}{1-2\ln x}\le 1$ $\frac{{{e}^{x}}-1}{1-2{{e}^{x}}}\le 1$

Accepted Answer

$x < \frac{1}{2}$ or $x\ge \frac{2}{3}$ (i) $-\frac{1}{2} < x <\frac{1}{2}$ or $x\ge \frac{2}{3}$ or $x\le -\frac{2}{3}$ (ii) $x\ge {{e}^{\frac{2}{3}}}$ or $0< x < \sqrt{e}$ (iii) $x < \ln \frac{1}{2}$ or $x\ge \ln \frac{2}{3}$

Inequalities - Inequalities involving Substitution

Inequalities - Inequalities involving Substitution

Video Solution:

Solution:

Solution locked