can someone show me the steps to solve x/6=x/7+5

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can someone show me the steps to solve x/6=x/7+5

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

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