Question

How do you solve `\frac{14}{12}=\frac{1}{10^{6}}+\frac{x}{10}`?

Answer 1

`x = (35(10^5)-3)/(3(10^5))`

This is how I would answer the equation, I'm not sure how simplified you want it.

Explanation:

`14/12 = 1/10^6 + x/10`

Simplify both sides
`7/6 = 10^-6+(10^-1)x`

Take out the `10^-1` and move to the other side
`10*7/6 = 10^-5 + x`

Simplify the `70/6` and move the `10^-5` over
`35/3 - 1/10^5 = x`

Multiply each fraction by each other's denominator to give the same denominator
`(35/3(10^5))/(3(10^5)) - 3/(3(10^5)) = x`

Now just subtract!
`x = (35(10^5)-3)/(3(10^5))`

Answer 2

`x ~~ 11.6667`

Explanation:

If you have an equation which has fractions, you can get rid of them immediately by multiplying by the LCD to cancel the denominators.

`1/10^6+x/10 =12/10" "larr 12/10 =7/6`

`LCD = color(blue)(6 xx 10^6)`

`(color(blue)(6 xx 10^6)xx1)/10^6 +(color(blue)(6 xx 10^6)xx x)/10 = (color(blue)(6 xx 10^6)xx7)/6`

Simplify both sides:

`(color(blue)(6xx cancel10^6)xx1)/cancel10^6 +(color(blue)(6 xx 10^(cancel6 5))xx x)/cancel10 = (color(blue)(cancel6^1 xx 10^6)xx7)/cancel6`

This leads to:

`6+6xx10^5xx x=7xx10^6`

`" "6xx10^5xx x=7xx10^6 -6" "larr` now isolate `x`

`x =(7xx10^6 -6)/(6xx10^5`

`x = (7xx10^6)/(6xx10^5)-cancel6/(cancel6xx10^5)`

`x = 70/6 -1xx10^-5`

`x ~~11.6667`