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1. Need help with algebraic fraction equations please!
I have a method but whenever I substitute my answer for x it doesn't balance on both sides so I don't know what I'm doing wrong...

Here is the question:

3x+2/4 - 7 = 5/8

This was what I did:
1) found the LCM = 8
first multiplied everything by 8 so that:

24x+16/4-56 = 5

And then multiplied everything by 4 so that:

96x +64 -224 = 20

96x -160 = 20

96x = 20+160

96x = 180

x = 1.875

But when substituted for x, it doesn't equal 5/8 (0.625) ?

Please help! I have a lot more questions after this to work on so just need an example to help me.
Thank you
Last edited by OkashiAddict; 18-09-2012 at 22:04.
2. Re: Need help with algebraic fraction equations please!
?
3. Re: Need help with algebraic fraction equations please!
you'll kick yourself if I show you the mistake....
4. Re: Need help with algebraic fraction equations please!
(Original post by elldeegee)
?
no, the 4 is under both 3x+2 but not the -7.
5. Re: Need help with algebraic fraction equations please!

24x+16/4-56 = 5

And then multiplied everything by 4 so that:

96x +64 -224 = 20

It was right until this point. 16/4 =/= 64

16/4 = 4
6. Re: Need help with algebraic fraction equations please!
(Original post by Azzura)
you'll kick yourself if I show you the mistake....
7. Re: Need help with algebraic fraction equations please!
see above post
8. Re: Need help with algebraic fraction equations please!
(Original post by Azzura)
It was right until this point. 16/4 =/= 64

16/4 = 4
Oh no, it's not 2/4
9. Re: Need help with algebraic fraction equations please!
24x+16/4-56 = 5

And then multiplied everything by 4 so that:

96x +64 -224 = 20
This is wherre your problems lie.
when multiplying by 4, you don't need to multiply the 16 by 4 (Just like above, you didn't multiply the 5 on the RHS by 8)
So you should just get 96x +16 -224 = 20

It is also worth noting that because 16/4 = 4, there is no real need to multiply through by 4.
10. Re: Need help with algebraic fraction equations please!
x = 2.375
11. Re: Need help with algebraic fraction equations please!
(Original post by elldeegee)
This is wherre your problems lie.
when multiplying by 4, you don't need to multiply the 16 by 4 (Just like above, you didn't multiply the 5 on the RHS by 8)
So you should just get 96x +16 -224 = 20

It is also worth noting that because 16/4 = 4, there is no real need to multiply through by 4.
Ohhh I see because they're the same kind of term? Why is this? And does this apply all the time for these kinds of questions?
Thank you
12. Re: Need help with algebraic fraction equations please!
no, the 4 is under both 3x+2 but not the -7.
Ignore what i had said before.

As your original question wasnt laid out very well, did you have ?
13. Re: Need help with algebraic fraction equations please!
is this A level or GCSE?
14. Re: Need help with algebraic fraction equations please!
(Original post by elldeegee)
Ignore what i had said before.

As your original question wasnt laid out very well, did you have ?
Yes, that's the one!
15. Re: Need help with algebraic fraction equations please!
(Original post by Azzura)
is this A level or GCSE?
GCSE... I think... well I'm in year 10
16. Re: Need help with algebraic fraction equations please!
GCSE... I think... well I'm in year 10
yeah then it's GCSE
17. Re: Need help with algebraic fraction equations please!
Yes, that's the one!
So you have

This bit:
24x+16/4-56 = 5
is correct, except you SHOULD write it as :
(i realise you may be unable to use the latexing format on here, but when laying it out on paper, it is easy to make mistakes if you don't lay it out like this)

Spoiler:
Show
when showing it on here without using latex, write (24x + 16)/4 -56 = 5 in order to make it clear what is in the fraction and what isn't

Again, it is here where the mistake was made:
And then multiplied everything by 4 so that:
96x +64 -224 = 20
and the use of brackets would have made it much more easier

multipply through by 4, so the numerator stays the same, but multiply all other terms by 4:

carry on from here.
Last edited by elldeegee; 18-09-2012 at 22:27.
18. Re: Need help with algebraic fraction equations please!
(Original post by elldeegee)
So you have

This bit:
is correct, except you SHOULD write it as :
(i realise you may be unable to use the latexing format on here, but when laying it out on paper, it is easy to make mistakes if you don't lay it out like this)

Spoiler:
Show
when showing it on here without using latex, write (24x + 16)/4 -56 = 5 in order to make it clear what is in the fraction and what isn't

Again, it is here where the mistake was made:

and the use of brackets would have made it much more easier

multipply through by 4, so the numerator stays the same, but multiply all other terms by 4:

carry on from here.
So I only multiply by 4 to cancel out the denominator, but not the other terms? I don't really understand... could you please be clearer?

Thanks for your help so far
19. Re: Need help with algebraic fraction equations please!
(Original post by Azzura)
It was right until this point. 16/4 =/= 64

16/4 = 4
You had actually misunderstood what it was he was doing so he wasn't saying that 16/4 = 64, he was saying that as he was multiplying through by 4, 16 x 4 =6 :

(Original post by elldeegee)
This is wherre your problems lie.
when multiplying by 4, you don't need to multiply the 16 by 4 (Just like above, you didn't multiply the 5 on the RHS by 8)
So you should just get 96x +16 -224 = 20

It is also worth noting that because 16/4 = 4, there is no real need to multiply through by 4.
20. Re: Need help with algebraic fraction equations please!
(Original post by elldeegee)
So you have

This bit:
is correct, except you SHOULD write it as :
(i realise you may be unable to use the latexing format on here, but when laying it out on paper, it is easy to make mistakes if you don't lay it out like this)

Spoiler:
Show
when showing it on here without using latex, write (24x + 16)/4 -56 = 5 in order to make it clear what is in the fraction and what isn't

Again, it is here where the mistake was made:

and the use of brackets would have made it much more easier

multipply through by 4, so the numerator stays the same, but multiply all other terms by 4:

carry on from here.
x = 9.5
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