# Homework Help: Algebra problem

1. Jun 3, 2007

### david18

Hi I'm on this question where I have to find x:

3x+5 - 2x-1 = 3
4 6

and i ended up with 9x + 15 - 4x - 2 = 36
12 = 12

so i removed the 12s to leave me with 9x + 15 - 4x - 2 = 36

Now for my question:

When I am simplifying the left hand side; does it become 5x + 13 or 5x + 17 because if the equation should be written as (9x + 15) - (4x - 2) it would mean a -- which is a plus to make 5x + 17...

edit: for some reason the denominators havent come up where i wanted them to be. but its 3x + 5 all over 4 and 2x - 1 all over 6
and the second error is that both sides should have 12 as their denominators

2. Jun 3, 2007

### Stevedye56

I'm not really sure how the problem is supposed to read. is 4 the denominator of 3x+5 and 6 the denominator of -2x-1?

3. Jun 3, 2007

### hage567

I'm confused. Is this the original equation?

$$\frac{3x+5}{4} - \frac{2x-1}{6} = 3$$

4. Jun 3, 2007

### Stevedye56

$$\frac {3x+5} {4} - \frac {2x-1} {6}=3$$

Last edited: Jun 3, 2007
5. Jun 3, 2007

### Stevedye56

You beat me to it :(

6. Jun 3, 2007

### Stevedye56

Error with LaTeX.

So wait you have $$\frac {3x+5} {4}$$ and that is all divided by 12?

Last edited: Jun 3, 2007
7. Jun 3, 2007

### david18

yes the 2 equations you said are correct, thanks for sorting my one out

8. Jun 3, 2007

### Stevedye56

So then everything is divided by 12?

9. Jun 3, 2007

### Stevedye56

I think there is an error in your work. If both sides have a denominator of 12 are you referring to the left side and right side of the "=" sign. If so you would have $$\frac {3} {12}$$ not 36.

10. Jun 3, 2007

### david18

the original equation eventually became
9x + 15 - 4x - 2 (all divided by 12) = 36 (all divided by 12) when i simplified it.
This is because I multiplied the denominators to make them all become 12

then i would be able to multiple either side by 12 to leave the equation:

9x + 15 - 4x - 2 = 36

But the problem is whether that becomes 5x + 13 or 5x + 17 is what im wondering.

11. Jun 3, 2007

### david18

i think my message has become a bit too confusing lol. basically the question are the ones that you 2 said. The denominator of 12 bit only comes up after some steps. and if i want to make them all have equal denominators, in this case 12, it would mean i would write 3 as 36/12

12. Jun 3, 2007

### Stevedye56

Im totally confused to what is going on right now.

Last edited: Jun 3, 2007
13. Jun 3, 2007

### hage567

david18, where did the 12 come from? What were you trying to do, cross multiply? I honestly can't see how you got from your first equation to the second.

14. Jun 3, 2007

### david18

actually ive got it... it becomes 5x + 17 = 36 because i used the method that most people use... which is a lot better than my 'make everything have a denominator of 12' method...

instead if you just make the left hand side have a denominator of 12 and leave the right hand side as 3...

... means the left hand side becomes:

3(3x+5) - 2(2x-1) = 3
______________
........12

(ignore dots)
which means its -2 x -1 which is +2. Yeah the method i used was bad so I'll avoid it makes myself confused.

does it make sense to everyone now?

15. Jun 3, 2007

### Stevedye56

That's what I'm wondering also. :grumpy:

16. Jun 3, 2007

### david18

This is the correct question. The Lowest common denominator is 12.

17. Jun 3, 2007

### Stevedye56

Ok. Then you would have $$\frac {9x+15} {12} - \frac {4x-2} {12} = 3$$

Therefore

$$\frac {5x +17} {12} = 3$$

18. Jun 3, 2007

### hage567

OK, I see what you were doing.

19. Jun 3, 2007

### Stevedye56

This is right, correct?

20. Jun 3, 2007

### hage567

Yes, I come up with the same answer. Sorry.