Linear and quadratic inequalitiesEdexcel International A Level Maths: Mind map

Exam questions on Linear and quadratic inequalities

1. Consider the inequality $3x-7>5x+1$, where $x$ is a real number.
   Find the set of values of $x$ for which $3x-7>5x+1$ or $2x+6>0$.2 marks
2. The function $f(x)=x^2-2x-8$ is defined for real $x$.
   Find the set of values of $x$ for which $f(x)<0$ and $2x-1>0$.2 marks
3. A rectangular patio has width $x$ m and length $(x+6)$ m. Its area must be less than $55$ m$^2$, and its width must be greater than $2$ m.
   Show that $x^2+6x-55<0$ and hence find the range of possible values of $x$.3 marks