Inequalities - Inequalities involving Substitution
Inequalities - Inequalities involving Substitution
Solve, without using a calculator, \(\frac{x+1}{x-1}<4\). Hence, solve
- \(\frac{\left| x \right|+1}{\left| x \right|-1}<4\)
- \(\frac{\ln x+1}{\ln x-1}<4\)
- \(\frac{{{e}^{x}}+1}{{{e}^{x}}-1}<4\)
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Answer:(i) \(-1 < x < 1\) or \(x > \frac{5}{3}\) or \(x < -\frac{5}{3}\); (ii) \(0 < x < e\) or \(x > e^{\frac{5}{3}}\); (iii) \(x < 0\) or \(x > \ln\frac{5}{3}\)
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