anonymous
  • anonymous
can someone show me the steps to solve x/6=x/7+5
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
multiply with 6 and 7 than bring x to one side. voila
anonymous
  • anonymous
\[\frac{ x }{ 6 }=\frac{ x }{ 7 }+5\] to better understand here is the actual problem in the correct equation
anonymous
  • anonymous
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

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anonymous
  • anonymous
7x/42 - 6x/42 = 5 x/42=5 x=5(42)
calculusfunctions
  • 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?
anonymous
  • anonymous
so step 2 would look like x/7-x/6=5
anonymous
  • anonymous
yes
anonymous
  • anonymous
Then you make the denominators the same
anonymous
  • anonymous
which would be 42,
anonymous
  • anonymous
yes since 6 X 7 = 42
anonymous
  • anonymous
this is the part i get confused at
anonymous
  • anonymous
would it look like x/42?
anonymous
  • anonymous
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
anonymous
  • anonymous
ahhh ok
anonymous
  • anonymous
so then is x/42=5
anonymous
  • anonymous
Yup
anonymous
  • anonymous
and then simplify from there
anonymous
  • anonymous
yup :)
anonymous
  • anonymous
how do i get x by itself?
anonymous
  • anonymous
move the 42 over to the other side by timesing both sides by 42.
anonymous
  • anonymous
|dw:1349349298325:dw|
anonymous
  • anonymous
42(x/42) = 5(42) x =210
anonymous
  • anonymous
thank you so much.. fractions is one thing i have an issue with..
anonymous
  • anonymous
that's fine :)
anonymous
  • anonymous
i have even harder ones... like \[\frac{ x}{ 2x+2 }=\frac{ -2x }{ 4x+4 }+\frac{ 2x-3 }{ x+1 }\]
anonymous
  • anonymous
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
anonymous
  • anonymous
\[{-2x \over 4(x+1)} + {4(2x-3) \over 4(x+1)}\]
anonymous
  • anonymous
and add them \[-2x + 8x -12 \over 4(x+1)\]
anonymous
  • anonymous
do the same with the other side and use 2(x+1) as denominator
anonymous
  • anonymous
\[{x \over 2(x+1)} = {6x -12 \over 4(x+1)}\]
anonymous
  • anonymous
and cross multiply for simplification
anonymous
  • anonymous
2x(x+1) = (6x-12) (x+1)
anonymous
  • anonymous
cancel the x+1 and you have 2x = 6x-12
anonymous
  • anonymous
and that is simplified as -4x = -12 which means x = 3
anonymous
  • anonymous
understand?
anonymous
  • anonymous
i believe so
anonymous
  • anonymous
great :)
anonymous
  • anonymous
i have one more fraction if anyone is interested in helping
anonymous
  • anonymous
\[\frac{ 5 }{ y-4 }-\frac{ 8 }{ y-4 }=\frac{ 2 }{ y^2-16 }\]
anonymous
  • anonymous
it throws me off to add sqrt
anonymous
  • anonymous
um... you could do it like this: \[{-3 \over y-4} = {2 \over y^2 -16}\] \[{-3 \over y -4} = {2 \over (y+4)(y-4)}\]
anonymous
  • anonymous
Then knock off the y-4 so you're left with \[-3 = {2 \over y+4}\]
anonymous
  • anonymous
and then use -3 (y+4) = 2 and simplify -3y - 12 = 2 -3y = 2 +12 -3y = 14 y = 14/-3
anonymous
  • anonymous
y = -(14/3)
anonymous
  • anonymous
wow that was easier than i thought
anonymous
  • anonymous
You were only stumped by the y^2 - 16 which is simplified as (y-4)(y+4)
anonymous
  • anonymous
thank you so much for helping me with these!
anonymous
  • anonymous
No probelma :)

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