Question

How do you solve `\frac { 11} { 2x } + \frac { 5} { 4x } = \frac { 3} { 4}`?

Answer 1

See a solution process below:

Explanation:

First, multiply the fraction `11/(2x)` by the appropriate form of `1` to have a common denominator for the two fractions on the left side of the equation:

`(2/2 xx 11/(2x)) + 5/(4x) = 3/4`

`(2 xx 11)/(2 xx 2x) + 5/(4x) = 3/4`

`22/(4x) + 5/(4x) = 3/4`

Next, add the two fractions on the left side of the equation:

`(22 + 5)/(4x) = 3/4`

`27/(4x) = 3/4`

Then, multiply each side of the equation by `color(red)(4)/color(blue)(3)` to eliminate the fraction on the right side of the equation while keeping the equation balanced:

`color(red)(4)/color(blue)(3) xx 27/(4x) = color(red)(4)/color(blue)(3) xx 3/4`

`cancel(color(red)(4))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(27))9)/(color(red)(cancel(color(black)(4)))x) = cancel(color(red)(4))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(4)))`

`9/x = 1`

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

`color(red)(x) xx 9/x = color(red)(x) xx 1`

`cancel(color(red)(x)) xx 9/(color(red)(cancel(color(black)(x)))) = x`

`9 = x`

`x = 9`