Question

How do you solve `1/3 - x/7 = 14/54`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(1/3)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`1/3 - color(red)(1/3) - x/7 = 14/54 - color(red)(1/3)`

`0 - x/7 = 14/54 - (18/18 xx color(red)(1/3))`

`-x/7 = 14/54 - 18/54`

`-x/7 = (14 - 18)/54`

`-x/7 = -4/54`

`-x/7 = -2/27`

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

`color(red)(-7) xx x/-7 = color(red)(-7) xx -2/27`

`cancel(color(red)(-7)) xx x/color(red)(cancel(color(black)(-7))) = 14/27`

`x = 14/27`

Answer 2

This is how we do it .

Explanation:

`1/3-x/7=14/54`

Take `-x/7` in the right so it will become `+x/7` . And take `14/54`on the left and it will become `-14/54`.
:. `1/3-14/54=x/7`

Then first solve `1/3-14/54` so , to solve you need to make the denominator same this is done by taking the LCM of `3`and `54`. That is 54 .

:. `1xxcolor(red)18` `/` `3xxcolor(red)18` `-` `14xxcolor(red)1` `/` `54xxcolor(red)1`
`:.` `18/54` `-` `14/54` `=x/7`
`:.` `4/54=x/7`
`:.` `4/54xx7` `=x`