Question

How do you solve `\frac { x } { 7} - \frac { x } { 3} = \frac { 2} { 3}`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(21)` to eliminate the fractions while keeping the equation balanced. `color(red)(21)` is the Lowest Common Denominator (LCD) for the 3 fractions:

`color(red)(21)(x/7 - x/3) = color(red)(21) xx 2/3`

`(color(red)(21) xx x/7) - (color(red)(21) xx x/3) = cancel(color(red)(21))7 xx 2/color(red)(cancel(color(black)(3)))`

`(cancel(color(red)(21))3 xx x/color(red)(cancel(color(black)(7)))) - (cancel(color(red)(21))7 xx x/color(red)(cancel(color(black)(3)))) = 14`

`3x - 7x = 14`

Next, combine like terms:

`(3 - 7)x = 14`

`-4x = 14`

Now, divide each side of the equation by `color(red)(-4)` to solve for `x` while keeping the equation balanced:

`(-4x)/color(red)(-4) = 14/color(red)(-4)`

`(color(red)(cancel(color(black)(-4)))x)/cancel(color(red)(-4)) = -7/2`

`x = -7/2`