Algebraic inequalitiesEdexcel A-Level Further Maths: Mind map

Exam questions on Algebraic inequalities

1. The inequality $\frac{x-1}{x+2}<2$ is to be solved, where $x\neq-2$.
   The student's method gives $x-1<2(x+2)$, which leads to $x>-5$. Show that $x=-3$ satisfies $x>-5$ but is not a solution of the original inequality, and explain the error.2 marks
2. The inequality $|2x-3|<x+4$ is to be solved.
   Hence solve $|2x-3|\geq x+4$.2 marks
3. Consider the inequality $\frac{3}{x-2}>\frac{2}{x+1}$, where $x\neq2$ and $x\neq-1$.
   Show that the inequality is equivalent to $(x-2)(x+1)(x+7)>0$.3 marks