## How to solve linear equations .. some of them you’ll solve without really thinking about!

Suppose you bought a CD for £8 and then two books at the same price. The total cost is £25 and, with a little bit of arithmetic, you might work out the price of each book is £8.50.

Mathematicians like to call these “linear equations” and they look something like:

2B + 8 = 25

(where ‘B’ stands for ‘books’)

#### Working with linear equations can get a little complex and there are a couple of rules:

- work down the page
- put the equals sign in the middle
- always remain in balance
- whatever you do to one side – you need to do to the other

##### Click here to try the quick test QT Linear Equations

Most of the exam questions for linear equations are based on

- mobile phone contracts
- temperature conversion
- salaries
- travel money

They are all much the same and usually involve comparing two offers.

Here’s some brief notes:

##### Mobile phones

Always a favourite and goes something like

“A plan costs £30 per month plus 1p per message – write a linear equation”

The monthly cost would be: 0.01 x total messages + 30 or, tidying up and written as a linear equation:

£ = 0.01M + 30

(Note the conversion to the same units ie 1p per message = £0.01 per message)

##### Temperature conversion

Converting Fahrenheit into degrees Celsius is an example of a linear function. You need to subtract 32 from the Fahrenheit and the multiply the result by 5/9. There are a couple of different ways of writing this formula but it amounts to the same calculation.

So

Degrees C = (5/9) x (F – 32)

or

Degrees C = (F – 32) / 1.8

##### Salaries

Something along the lines of

“You get paid £8 per hour and work for ‘x’ hours per week. Tax is 8% of your pay. Write a linear equation to describe your pay.”

Which means

Total pay = 8’x’ – 8%

or, tidying up:

Total Pay = 0.92 ( 8 ‘x’ )

as it’s neater to multiply by 0.92, which is the decimal equivalent of 100% – 8% … although the first equation is fine.

##### Money

Fairly typically a currency conversion such as dollars $ to pounds £. As of beginning October 2012 there were $1.6074 to the £ so a linear equation would be:

£ = 1.6074 x $

or, tidying up:

£ = 1.6074$

#### Watch on YouTube

How to solve linear equations with brackets

How to solve linear equations with ‘x’ on both sides

How to solve linear equations with fractions

How to solve linear equations with fractions and brackets

Ann Narte says

LOve the tutorial .. i understand clearly .. and really helpful for

advanced idea 😉 thanks for this 🙂

Anupreet Dhanju says

easy to understand, thanks, its big help for my exam

Blaze heh says

Thanks a lot and is the other way to solve this is when you take the

numbers and put it on the other side

Abdulkadir Omar says

Hello is any one can help me this

-(c-8)= -2

Rami Ghassan says

Thank you very much but does this method apply for this type of an equation

(x/2)+(x-2)/3 <5?

Pat Motley says

Thank you, I hope this will go towards getting a B in my exam

JEDIandMUSHplayMC says

thanks man you make a lot of sense explaining this to me heck i was not

bored out of my mind like + Subscribe!

Nighat Loon says

How about something like 4(6x + 2) = 2 (3x/4 + 5)?

Tara Oloughlin says

Need help with this question

3(2-x)-4(3-2x)=14

cant seem to find any examples

Karen x says

Thanks for the help! You explain it very clearly and you write down EACH

AND EVERY STEP which is soo soooo soooo helpful! My teacher does it all in

his head and skips steps- but he forgets that his students aren’t all

professional maths teachers like himself too and we cant keep up :'(

cyriptobi137 says

Thanks for all the videos they really helped in my gcse mock test that I

took today, it was very hard but the stuff I learnt in these videos allowed

me to answer lots of questions that I wouldnt have been able to answer

before.

TheXCore360 says

Sorry if I sound stupid but why did you divide by -8? And in what other

situations can you do what you that?

xoarianagrandes says

getting into basic algebra & my teacher is going WAY too fast!! failed my

test today and got a 2 out of 12. just saw your videos & they are really

helping me! your tutorials are great and you aren’t going too fast or slow.

can you do a video on like when it says the linear expression in words &

you have to figure out the equation, then solve for x? (:

Birthday N says

Again, thanks for the help! You’re great!

duha mani says

your method is quite difficult 🙁 just spreat them

Catherine Cletus says

Thankyou so much this helped me soo much!! Without you I couldn’t of done

this without you!! Thankyou so much!!!!!! :):)

Mateen Malik says

Hello Simon at 3:29 isn’t the fraction is suppose to be multiplied by 4?

Michael Shiels says

Thanks! I have a test in 3 days and I didn’t get it till now 🙂

Jj Soyo says

Bruhh. What is he saying.

Rhett Wiley says

What if there are two fractions on one side, and one on the other.

Different denominators. 2x+5/5 + x-7/2 = 3x+1/2? I’m confused on

multiplying the both sides, and then dividing them out?

alexis kingston says

this hlps a lot i wudnt be pt out of class for nt doing my home-work anymre

lol thxs

RadiantRadeon says

Why cant there be more teachers like this guy. Thanks Simon for the lesson!

yassin b says

thanks! really helpful 🙂

SarahEKlas says

What do you do if there is a minus sign before the bracket such as

5-(x-4=22?

Joe Doe says

Why don’t you multiply 29 by 4 at the beginning?

skill kickerz says

thanks so much missed, this lesson in math class!

axelNodvon2047 says

Please help

5( 1/2x -1) = 1/4( 6x + 8)

Jeremiah Choi says

U ARE THE BEST!!!!!! MY SCHOOL ONLY DID MY HEAD IN TRYING TO EXPLAIN THIS

Aarin Henning says

Im in a very high level math class and I sometimes get stumped by long

simple equations, I will probably figure out what I did wrong in a couple

hours but heres the equation.

3{2-3(2n+4-3n)}+5n=4n-2(n-5) Algebra II btw. The answer is 10/3 but I cant

figure out how I get that answer -_-

mahalika Williams says

i cant watch this because he talk alot

hadi farrukh says

Really really helpful…thank you so much!!!

Parmanand Choudhary says

thanks buddy- U made me understand this!

Antonino Mineo says

he is a saver..

Antonino Mineo says

I get positive 11, because I would move both right’s hand side factors to

the left at once and then carry out the operation

MAJORSNODGRASS says

Why are equations described as linear?

Gabriel24blu says

This guy looks like ted benekee

biggyBeatV3 says

Nice!

TheEmptyCar says

Can you help me answer this equation?

8x-5 (x+4) = 0

joelywoel says

Hi Simon. Really struggling with 9 (2x – 1) = 4 (5x – 4), question 2 on

the quick foundation test. Thanks for all the help. Any ideas anyone?

heeheje hej says

can please help

2x+3 = 2x+1

Angelo Kolokotronis says

can u help me with 1/2-1/x=1-x squared-x

Areeb Fardin says

Can u help me with this question please

5 ( 2x -1 ) =16x

Brandon Adams says

MYYYYYYYYYYYYYYYYYYNussssssss

matthew bacon says

thx

khuram hussain says

5x+y-3y+6x is this y=11 or y=7.5 please reply I got this by 5x+6x=11X and

3y=11

Wong Ming Hao says

Can you help in math

Can you be my math teacher by posting these video

ok?

RosePru says

Thank you for the prompt reply. I appreciate it fully. Looking forward to

more videos…

RosePru says

Thank you for the prompt reply. I appreciate it fully. Looking forward to

more videos…

RosePru says

3x.x= 5x -2

RosePru says

3x.x= 5x -2

Josue Hidalgo says

multiplying x/3 by 3 makes it 1x or x ? why?how? what is this witchcraftery

, please explain

Mohammed Motaz alsahen says

x=2

Francesco Del Colombo says

2x+2=5x-4

x= ?

Please Im really getting crazy with this.

Syed Shaban says

Athis helped me extremely

The Global Excursion says

Thanks for your help

Freya Nair says

very good tutorial! really appreciate it!

Akbar Toryalae says

Thanks

Good teacher

DefenseHamster says

Thanks. They told us to do this for homework without explaining how to do it.

Christopher Tucker says

Helped me a lot thanks

Simon Deacon says

Glad to help 🙂

Chad Modernel says

thanks sooo much !

fiberkinetics says

bye bye fraction

Simon Deacon says

Hi Kailee – there’s a post on mathswrap.co.uk that has all the videos on one page. If you visit the site and search for ‘linear equations’ there’s 7 videos and a quick test to try. Hope this is all OK please let me know if it helps – thanks 🙂

Kailee Goertzen says

Would you mind doing another video going more in depth about how to do it. I still don’t quite understand.

Simon Deacon says

Hi – ok, if you post the specific problem we can work through. S

DerpingTurtle says

this did not work 🙁

shoptrot says

Thats an equation, not a linear equation

Simon Deacon says

That’s great – thanks for letting me know 🙂

Nikefan500000 says

Thankyou! This is just what I need

Simon Deacon says

Hi – glad it helped :-). I’m a maths tutor and run three First Class Learning centres.

Jeremy Moulton says

Cheers Simon! Top lad! Are you a teacher?

Sam Shewbridge says

you’re a good teacher! thank you

Lea Keohane says

Thank you! I’m helping my 7th grader with her homework and it’s been around 25 years since I’ve had to do this myself 😉

marioladolphin says

Wow Thanks 🙂 Plus Im 1st Comment, Haha! You Saved Me From My Evil Maths Teacher… o.o

DerriAndBailey says

i don’t get it.

1AirTech says

Thanks teacher ur great keep up with the vids;)