Review practice · Section 2 of 3

Without using a calculator, solve the inequality $\dfrac{3x}{2x^2-3x+1}>-1$.4 marks

Hence solve $\dfrac{3|x|}{2x^2-3|x|+1}>-1$.3 marks

(a) Using an algebraic method, solve the inequality $\dfrac{x+4}{3+2x-x^2}<1$.5 marks

(b) Hence solve the inequality $\dfrac{x^2-4}{x^4+2x^2-3}<1$.2 marks

Do not use a calculator in answering this question.

Solve the inequality $\dfrac{x+4}{-x^2+2x+3}<1$.4 marks

Deduce the solution of

(i) $\dfrac{x^2+4}{-x^4+2x^2+3}<1$,2 marks

(ii) $\dfrac{x-4}{x^2+2x-3}<1$.2 marks

Find the solution sets of the following inequalities.

(a) $x^2<|x-2|$,

(b) $\left|\dfrac{x+1}{3x-5}\right|>1$.

Solve the inequality $x+5<|2x-1|+|x-3|$.5 marks

Solve graphically the inequality $|x+2|\geq\ln(x^2-2x+1)$.4 marks