# Inequalities

Ghaah, I LOVE INEQUALITIES 😀 One of my favourite topics I have to admit. To be quite honest though… I’m not a complete fan with algebra but these are one of my rare topics which I enjoy! 😀 Looks scary doesn’t it? That question on the left? Eh?

C’mon, admit it, the first time I saw this question I was as scared as hell but if you actually *know *how to work this thing, you’ll find it a piece of cake. Want to know how to do it? Well this is the place for you! 😀

*Things you need to remember:*

**>** = more than

**<** = less than

**≥** = greater than or equal to

**≤** = less than or equal to

^^ This is important in this topic.

*And…*

**B** = Brackets

**I** = Indices

**D** = Division

**M** = Multiplication

**A** = Addition

**S** = Subtraction

Ok, step 1:

4*x* + 3 > 2(3*x* – 1)

^^ you see that, right? Ok *sigh* we need to get through this.

You know how to expand brackets, right? Because if you don’t… then you shouldn’t be on this page right now, you should be on a DIFFERENT page. Anyway, expanding the brackets. In order to make the question simpler for you, you *have to *expand the brackets on the right hand side of the question and if two brackets take place in both sides *the brackets ALWAYS come first*. Got it?

So first come the brackets and you *can’t *switch them around the way you want otherwise your answer will turn out completely and utterly wrong.

Ok, anyway, the brackets.

2(3*x*-1), piece of cake! You times 2 by 3*x* which equals **6 x** and then you multiply 2 by -1 which also equals -2. RESULT:

**6**

*x*-2.So now you’ve expanded the brackets.

**4 x + 3 > 6x – 2**

Ok, now here it’s when it gets easy. Do you know how to balance equations? Because if you do you’ll find this *seriously easy.* Nothing to worry about for you. Imagine this symbol ‘ >’ as a ‘=’ sign so you won’t get confused. So it will be planned like this: **4 x + 3 = 6x – 2 **

*(or if you prefer… the symbol may come back to this anyway…)*

Balancing it *all *out:

**4 x + 3 = 6x – 2**

*(remember, what you do to one side, you do to the other)*

* ***+ 2 4 x + 3 = 6x – 2 + 2**

*(getting rid of the ‘2’ makes…)*

**4 x + 5 = 6x**

*(Now what do you do? Balance it out, right?)*

**– 4 x 4x + 5 = 6x – 4x**

*(This results as…)*

**5 = 2 x**

*(What do you do to get it to ONE ‘x’?)*

**5 ÷ 2 = 2.5**

*(And that results as your answer which is…)*

*x* = 2.5

Woop