Question

How do you solve `\frac { 21} { 56} = 3/x`?

Answer 1

See a solution process below:

Explanation:

First, we can reduce the fraction on the left side of the equation:

`(7 * 3)/(7 * 8) = 3/x`

`(color(red)(cancel(color(black)(7))) * 3)/(color(red)(cancel(color(black)(7))) * 8) = 3/x`

`3/8 = 3/x`

Because both sides of the equation are pure fractions we can flip the fractions to rewrite the equation as:

`8/3 = x/3`

Now, multiply each side of the equation by `color(red)(3)` to solve for `x` while keeping the equation balanced:

`color(red)(3) xx 8/3 = color(red)(3) xx x/3`

`cancel(color(red)(3)) xx 8/color(red)(cancel(color(black)(3))) = cancel(color(red)(3)) xx x/color(red)(cancel(color(black)(3)))`

`8 = x`

`x = 8`

After reducing the fractions, we also observe the numerator of both fractions are the same and therefore the denominators must be the same if they are equal:

`color(red)(3)/8 = color(red)(3)/x`

Therefore:

`8 = x` or `x = 8`