## boomerang285 3 years ago can someone show me the steps to solve x/6=x/7+5

1. carl_gauss

multiply with 6 and 7 than bring x to one side. voila

2. boomerang285

$\frac{ x }{ 6 }=\frac{ x }{ 7 }+5$ to better understand here is the actual problem in the correct equation

3. order

Move the x's to one side. Make the denominators equal. Minus the two terms, and move the denominator over to the over side and multiply 5 by the denominator (42) and then divide by the number next to x on the side where 5(42) is. and voila

4. order

7x/42 - 6x/42 = 5 x/42=5 x=5(42)

5. calculusfunctions

$\frac{ x }{ 6 }=\frac{ x }{ 7 }+5$ Multiply both sides by 42 (least common multiple of 6 and 7), to obtain 7x = 6x + 210 ∴ x = 210 Do you understand?

6. boomerang285

so step 2 would look like x/7-x/6=5

7. order

yes

8. order

Then you make the denominators the same

9. boomerang285

which would be 42,

10. order

yes since 6 X 7 = 42

11. boomerang285

this is the part i get confused at

12. boomerang285

would it look like x/42?

13. order

but in order to make the denominators equation, you need to times the numerator by the amount that the denominator needs to make 42. eg. 6 X ? = 42 (7) so times the top x by 7 which becomes 7x. and the other becomes 6x since you need to times 7 by 6 to make 42. so it would be 7x/42 - 6x/42 7x-6x = x so it will eventually become x/42

14. boomerang285

ahhh ok

15. boomerang285

so then is x/42=5

16. order

Yup

17. boomerang285

and then simplify from there

18. order

yup :)

19. boomerang285

how do i get x by itself?

20. order

move the 42 over to the other side by timesing both sides by 42.

21. magepker728

|dw:1349349298325:dw|

22. order

42(x/42) = 5(42) x =210

23. boomerang285

thank you so much.. fractions is one thing i have an issue with..

24. order

that's fine :)

25. boomerang285

i have even harder ones... like $\frac{ x}{ 2x+2 }=\frac{ -2x }{ 4x+4 }+\frac{ 2x-3 }{ x+1 }$

26. order

You use the same principle: so to add two fractions, the denominators must be the same. make the denominator under -2x simplified: 4x + 4 4(x+1) and use {-2x over 4(x+1)} + {4(2x-3) over 4(x+1)} as a first step

27. order

${-2x \over 4(x+1)} + {4(2x-3) \over 4(x+1)}$

28. order

and add them $-2x + 8x -12 \over 4(x+1)$

29. order

do the same with the other side and use 2(x+1) as denominator

30. order

${x \over 2(x+1)} = {6x -12 \over 4(x+1)}$

31. order

and cross multiply for simplification

32. order

2x(x+1) = (6x-12) (x+1)

33. order

cancel the x+1 and you have 2x = 6x-12

34. order

and that is simplified as -4x = -12 which means x = 3

35. order

understand?

36. boomerang285

i believe so

37. order

great :)

38. boomerang285

i have one more fraction if anyone is interested in helping

39. boomerang285

$\frac{ 5 }{ y-4 }-\frac{ 8 }{ y-4 }=\frac{ 2 }{ y^2-16 }$

40. boomerang285

it throws me off to add sqrt

41. order

um... you could do it like this: ${-3 \over y-4} = {2 \over y^2 -16}$ ${-3 \over y -4} = {2 \over (y+4)(y-4)}$

42. order

Then knock off the y-4 so you're left with $-3 = {2 \over y+4}$

43. order

and then use -3 (y+4) = 2 and simplify -3y - 12 = 2 -3y = 2 +12 -3y = 14 y = 14/-3

44. order

y = -(14/3)

45. boomerang285

wow that was easier than i thought

46. order

You were only stumped by the y^2 - 16 which is simplified as (y-4)(y+4)

47. boomerang285

thank you so much for helping me with these!

48. order

No probelma :)