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
LOve the tutorial .. i understand clearly .. and really helpful for
advanced idea 😉 thanks for this 🙂
easy to understand, thanks, its big help for my exam
Thanks a lot and is the other way to solve this is when you take the
numbers and put it on the other side
Hello is any one can help me this
-(c-8)= -2
Thank you very much but does this method apply for this type of an equation
(x/2)+(x-2)/3 <5?
Thank you, I hope this will go towards getting a B in my exam
thanks man you make a lot of sense explaining this to me heck i was not
bored out of my mind like + Subscribe!
How about something like 4(6x + 2) = 2 (3x/4 + 5)?
Need help with this question
3(2-x)-4(3-2x)=14
cant seem to find any examples
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 :'(
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.
Sorry if I sound stupid but why did you divide by -8? And in what other
situations can you do what you that?
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? (:
Again, thanks for the help! You’re great!
your method is quite difficult 🙁 just spreat them
Thankyou so much this helped me soo much!! Without you I couldn’t of done
this without you!! Thankyou so much!!!!!! :):)
Hello Simon at 3:29 isn’t the fraction is suppose to be multiplied by 4?
Thanks! I have a test in 3 days and I didn’t get it till now 🙂
Bruhh. What is he saying.
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?
this hlps a lot i wudnt be pt out of class for nt doing my home-work anymre
lol thxs
Why cant there be more teachers like this guy. Thanks Simon for the lesson!
thanks! really helpful 🙂
What do you do if there is a minus sign before the bracket such as
5-(x-4=22?
Why don’t you multiply 29 by 4 at the beginning?
thanks so much missed, this lesson in math class!
Please help
5( 1/2x -1) = 1/4( 6x + 8)
U ARE THE BEST!!!!!! MY SCHOOL ONLY DID MY HEAD IN TRYING TO EXPLAIN THIS
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 -_-
i cant watch this because he talk alot
Really really helpful…thank you so much!!!
thanks buddy- U made me understand this!
he is a saver..
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
Why are equations described as linear?
This guy looks like ted benekee
Nice!
Can you help me answer this equation?
8x-5 (x+4) = 0
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?
can please help
2x+3 = 2x+1
can u help me with 1/2-1/x=1-x squared-x
Can u help me with this question please
5 ( 2x -1 ) =16x
MYYYYYYYYYYYYYYYYYYNussssssss
thx
5x+y-3y+6x is this y=11 or y=7.5 please reply I got this by 5x+6x=11X and
3y=11
Can you help in math
Can you be my math teacher by posting these video
ok?
Thank you for the prompt reply. I appreciate it fully. Looking forward to
more videos…
Thank you for the prompt reply. I appreciate it fully. Looking forward to
more videos…
3x.x= 5x -2
3x.x= 5x -2
multiplying x/3 by 3 makes it 1x or x ? why?how? what is this witchcraftery
, please explain
x=2
2x+2=5x-4
x= ?
Please Im really getting crazy with this.
Athis helped me extremely
Thanks for your help
very good tutorial! really appreciate it!
Thanks
Good teacher
Thanks. They told us to do this for homework without explaining how to do it.
Helped me a lot thanks
Glad to help 🙂
thanks sooo much !
bye bye fraction
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 🙂
Would you mind doing another video going more in depth about how to do it. I still don’t quite understand.
Hi – ok, if you post the specific problem we can work through. S
this did not work 🙁
Thats an equation, not a linear equation
That’s great – thanks for letting me know 🙂
Thankyou! This is just what I need
Hi – glad it helped :-). I’m a maths tutor and run three First Class Learning centres.
Cheers Simon! Top lad! Are you a teacher?
you’re a good teacher! thank you
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 😉
Wow Thanks 🙂 Plus Im 1st Comment, Haha! You Saved Me From My Evil Maths Teacher… o.o
i don’t get it.
Thanks teacher ur great keep up with the vids;)