Question

How do you solve `\frac { 1} { x } + \frac { 1} { 6} = \frac { 1} { 2}`?

Answer 1

See the solution process below:

Explanation:

First, subtract `color(red)(1/6)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`1/x + 1/6 - color(red)(1/6) = 1/2 - color(red)(1/6)`

`1/x + 0 = (3/3 xx 1/2) - color(red)(1/6)`

`1/x = (3 xx 1)/(3 xx 2) - color(red)(1/6)`

`1/x = 3/6 - color(red)(1/6)`

`1/x = (3 - 1)/6`

`1/x = 2/6`

`1/x = (2 xx 1)/(2 xx 3)`

`1/x = (cancel(2) xx 1)/(cancel(2) xx 3)`

`1/x = 1/3`

Now, multiply each side of the equation by `3x` to eliminate the fractions and solve for `x` while keeping the equation balanced:

`3x * 1/x = 3x * 1/3`

`3color(red)(cancel(color(black)(x))) * 1/color(red)(cancel(color(black)(x))) = color(blue)(cancel(color(black)(3)))x * 1/color(blue)(cancel(color(black)(3)))`

`3 * 1 = x * 1`

`3 = x`

`x = 3`