# Solving inequalities

#### IceDancer91

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?

#### tomjackson

I was completely surprised by seeing all these meshes especially the triparts insert mesh.

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#### mthCCC2013

Greatly appreciated.

#### Dacu

Hello!
Solve the inequality $$\displaystyle 3x^2+4ix+5<0$$ , where $$\displaystyle i^2=-1$$.
Thank You!

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#### Julian21

Thank you so much nice tutorial.

#### Bonganitedd

I have trouble solving inequalities especially quadratic. My main problem is presenting critical points. I hope you attachment will solve my problem. Thank you

#### Dacu

I have trouble solving inequalities especially quadratic. My main problem is presenting critical points. I hope you attachment will solve my problem. Thank you
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 $$\displaystyle d\leq 0$$.

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