Question

How do you solve `x/6 = x/7 + 5`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(42)` to eliminate the fractions while keeping the equation balanced. `color(red)(42)` (or `7 xx 6`) is the Least Common Denominator for the two fractions:

`color(red)(42) xx x/6 = color(red)(42)(x/7 + 5)`

`cancel(color(red)(42)) 7 xx x/color(red)(cancel(color(black)(6))) = (color(red)(42) xx x/7) + (color(red)(42) xx 5)`

`7x = (cancel(color(red)(42)) 6 xx x/color(red)(cancel(color(black)(7)))) + 210`

`7x = 6x + 210`

Now, subtract `color(red)(6x)` from each side of the equation to solve for `x` while keeping the equation balanced:

`-color(red)(6x) + 7x = -color(red)(6x) + 6x + 210`

`(-color(red)(6) + 7)x = 0 + 210`

`1x = 210`

`x = 210`