Question

How do you solve `\frac { n - 10} { 6} = \frac { 10} { 7}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(42)` to eliminate the fractions. `color(red)(42)` is the Lowest Common Denominator for the two fractions:

`color(red)(42) xx (n - 10)/6 = color(red)(42) xx 10/7`

`cancel(color(red)(42))7 xx (n - 10)/color(red)(cancel(color(black)(6))) = cancel(color(red)(42))6 xx 10//color(red)(cancel(color(black)(7)))`

`7(n - 10) = 60`

`(7 xx n) - (7 xx 10) = 60`

`7n - 70 = 60`

Next, add `color(red)(70)` to each side of the equation to isolate the `n` term while keeping the equation balanced:

`7n - 70 + color(red)(70) = 60 + color(red)(70)`

`7n - 0 = 130`

`7n = 130`

Now, divide each side of the equation by `color(red)(7)` to solve for `n` while keeping the equation balanced:

`(7n)/color(red)(7) = 130/color(red)(7)`

`(color(red)(cancel(color(black)(7)))n)/cancel(color(red)(7)) = 130/7`

`n = 130/7`