Solve the inequality \(\dfrac{{4x}}{{x - 2}} \ge 1\).

Solve the inequality \(\dfrac{1}{x} > \dfrac{1}{{x - 1}}\).

Solve the inequality \(\dfrac{{2 - {x^2}}}{x} > 1\).

The solutions to \(\dfrac{x}{{x + 1}} > 0\) are? 

The solutions to \(\dfrac{{x - 3}}{{x + 2}} > 1\) are? 

The solutions to \(\dfrac{3}{{1 - x}} \le 2\) are? 

The solutions to \(\dfrac{{{x^2}}}{{{x^2} - 1}} \le 1\) are? 

The solutions to \(\dfrac{{x - 1}}{{x + 1}} + 1 < 0\) are? 

(i) On a number plane, sketch the graphs of \(y=5-2 x\) and \(y=\dfrac{2}{x}\).

(ii) Using part (i) or otherwise write down the values of \(x\) for which \(5-2 x<\dfrac{2}{x}\)

(i) On a number plane, sketch the graphs of \(y=x+2\) and \(y=\dfrac{2 x}{x-1}\).

(ii) Using part (i) or otherwise write down the values of \(x\) for which \(x+2>\dfrac{2 x}{x-1}\)

Solve the inequality \(\dfrac{2-x}{x} \geq 1\)

Solve the inequality \(\dfrac{x+1}{x-2} \leq 2\)

(i) On a number plane sketch the graphs of \(y=1-x\) and \(y=\dfrac{1-3 x}{1+3 x}\).

(ii) Using part (i) or otherwise write down the values of \(x\) for which \(1-x>\dfrac{1-3 x}{1+3 x}\)

Solve the inequality \(\dfrac{1}{x+1}+\dfrac{1}{x}<\dfrac{1}{x(x+1)}\)

Solve the inequality \(\dfrac{x-1}{x+2} \leq \dfrac{x-2}{x+1}\)