Question

How do you solve `\frac { 3} { 5} + \frac { 1} { 2} = \frac { 1} { x }`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(10)color(blue)(x)` to eliminate the fractions. `10x` is the common denominator for all of the fractions:

`color(red)(10)color(blue)(x)(3/5 + 1/2) = color(red)(10)color(blue)(x) xx 1/x`

`(color(red)(10)color(blue)(x) xx 3/5) + (color(red)(10)color(blue)(x) xx 1/2) = color(red)(10)cancel(color(blue)(x)) xx 1/color(blue)(cancel(color(black)(x)))`

`(cancel(color(red)(10))2color(blue)(x) xx 3/color(red)(cancel(color(black)(5)))) + (cancel(color(red)(10))5color(blue)(x) xx 1/color(red)(cancel(color(black)(2)))) = 10`

`6x + 5x = 10`

Next, combine like terms on the left side of the equation:

`(6 + 5)x = 10`

`11x = 10`

Now, divide each side of the equation by `color(red)(11)` to solve for `x` while keeping the equation balanced:

`(11x)/color(red)(11) = 10/color(red)(11)`

`(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 10/11`

`x = 10/11`