Question

How do you solve `\frac { 26} { 65} = 2/x`?

Answer 1

See a couple of solution processes below:

Explanation:

Process 1:

multiply each side of the equation by `(color(red)(65)color(blue)(x))/color(green)(26)` to solve for `x` while keeping the equation balanced:

`(color(red)(65)color(blue)(x))/color(green)(26) xx 26/65 = (color(red)(65)color(blue)(x))/color(green)(26) xx 2/x`

`(cancel(color(red)(65))color(blue)(x))/cancel(color(green)(26)) xx color(green)(cancel(color(black)(26)))/color(red)(cancel(color(black)(65))) = (color(red)(65)cancel(color(blue)(x)))/(cancel(color(green)(26))13) xx color(green)(cancel(color(black)(2)))/color(blue)(cancel(color(black)(x)))`

`x = 65/13`

Process 2:

Because each side of the equation is a pure fraction we can flip the fractions:

`65/26 = x/2`

Now, multiply each side of the equation by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`color(red)(2) xx 65/26 = color(red)(2) xx x/2`

`cancel(color(red)(2)) xx 65/(color(red)(cancel(color(black)(26)))13) = cancel(color(red)(2)) xx x/color(red)(cancel(color(black)(2)))`

`65/13 = x`

`x = 65/13`