## boomerang285 Group Title can someone show me the steps to solve x/6=x/7+5 one year ago one year ago

1. carl_gauss Group Title

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

2. boomerang285 Group Title

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

3. order Group Title

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 Group Title

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

5. calculusfunctions Group Title

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

6. boomerang285 Group Title

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

7. order Group Title

yes

8. order Group Title

Then you make the denominators the same

9. boomerang285 Group Title

which would be 42,

10. order Group Title

yes since 6 X 7 = 42

11. boomerang285 Group Title

this is the part i get confused at

12. boomerang285 Group Title

would it look like x/42?

13. order Group Title

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 Group Title

ahhh ok

15. boomerang285 Group Title

so then is x/42=5

16. order Group Title

Yup

17. boomerang285 Group Title

and then simplify from there

18. order Group Title

yup :)

19. boomerang285 Group Title

how do i get x by itself?

20. order Group Title

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

21. magepker728 Group Title

|dw:1349349298325:dw|

22. order Group Title

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

23. boomerang285 Group Title

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

24. order Group Title

that's fine :)

25. boomerang285 Group Title

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

26. order Group Title

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 Group Title

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

28. order Group Title

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

29. order Group Title

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

30. order Group Title

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

31. order Group Title

and cross multiply for simplification

32. order Group Title

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

33. order Group Title

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

34. order Group Title

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

35. order Group Title

understand?

36. boomerang285 Group Title

i believe so

37. order Group Title

great :)

38. boomerang285 Group Title

i have one more fraction if anyone is interested in helping

39. boomerang285 Group Title

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

40. boomerang285 Group Title

it throws me off to add sqrt

41. order Group Title

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 Group Title

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

43. order Group Title

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

44. order Group Title

y = -(14/3)

45. boomerang285 Group Title

wow that was easier than i thought

46. order Group Title

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

47. boomerang285 Group Title

thank you so much for helping me with these!

48. order Group Title

No probelma :)