## anonymous 4 years ago how do you solve, x/2+x/5=x/6-1/3

1. eyust707

You bring all the terms with x's to one side and the numerical term to the other side. Then you find the least common multiple of the denominators. You multiply each term by the appropriate factor to make the denominators all have the same LCM. Then you add the terms. Finally you multiply each side by the denominator so that x is isolated.

2. anonymous

can you explain further?

3. theEric

Well, you want x to be on only one side of the equation when you're finished, so that's actually a good place to start.

4. theEric

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

5. anonymous

X=5/8???

6. anonymous

i put all the x values on one side and i made the LCD 60 is that good so far?

7. theEric

Correct, GeekChic_! 60 is a good denominator! 30 also works if you'd like, but 60 will be fine too!

8. anonymous

yea thats what i got but shouldn't it be -5/8?

9. anonymous

yea lol i meant 30 as LCD

10. theEric

So you have$\frac{30x}{60}+\frac{12x}{60}-\frac{10x}{60}=-\frac{1}{3}$

11. anonymous

yup

12. theEric

Oh yeah, definately$-\frac{5}{8}$

13. anonymous

$\frac{ 5x+2x }{ 10 }=\frac{ 3x-6 }{ 18 }$ then cross-multiply $18(5x+2x)=10(5x+2x)$

14. anonymous

x=-5/8

15. anonymous

alright thanks guys!

16. theEric

No problem! I'm glad you could work through the problem! Take care!