Practice section 6 of 7

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

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

Do not use a calculator in answering this question.

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

Deduce the solution of

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

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

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]

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

Solve the inequality $e^{\frac54x}+6\leq-2x^3-4x^2+5x+15$. [4]