Thank you, looks great!
This is very helpful but i am still stuck on a particular inequality. 2-3x<|x-3|. So far i have used the modular property and obtained a three term quadratic equation which further factorizes to (2x+1)(4x-5)<0. So according to me the answer is -1/2<x<5/4 but according to the marking scheme its only x>-1/2. Can somebody plz explain why?
Any inequality can be written as an equation and so $\displaystyle ax^2+bx+c\leq 0$ you can write the equation as $\displaystyle ax^2+bx+c=d\leq 0$.The solutions of the inequality are :
$\displaystyle x=\frac{-b\pm \sqrt{b^2-4a(c-d)}}{2a}$ where $\displaystyle d\leq 0$.