# 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.

21. Jun 3, 2007

### cepheid

Staff Emeritus
I don't understand what everybody is getting confused about! There is nothing wrong whatsoever with the method that you first tried to use, david18. Here's what you started with:

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

Then you put everything over a common denominator of 12:

$$\frac{9x+15}{12} - \frac{4x-2}{12} = \frac{36}{12}$$

So far, you're correct! Now, to answer the question in your original post, when you combine the two terms on the left hand side, you have to be careful! You are subtracting the whole second term from the first term. As a result, you must subtract the second numerator in its entirety from the first. To make sure you get this right, use parentheses:

$$\frac{9x+15 - (4x-2)}{12} = \frac{36}{12}$$

Now, when you remove the parentheses, be sure to get the signs right:

$$\frac{9x + 15 - 4x + 2}{12} = \frac{36}{12}$$

$$\frac{5x +17}{12} = \frac{36}{12}$$

Now, of course, you can multiply both sides by 12, which is equivalent to just removing the denominators:

$$5x +17 = 36$$

Can you see that this method is not different from the "second method" that you used? It doesn't matter whether you express the right hand side as 3 or 36/12. Mathematically, those are just two ways of writing the same number, and you'll still end up with 5x + 17 = 36 in the end. The two methods are not distinct from each other. They're the same.

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

### Stevedye56

What was so confusing was that it wasn't in latex and the spaces that were used to set up the fractions didn't come out. Also the method wasn't very clear.