Question

How do you solve `\frac { 2A } { 3} + \frac { 1} { 5} = \frac { 7} { 6}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(30)`, the lowest common denominator of the three fractions, to eliminate the fractions while keeping the equation balanced:

`color(red)(30)((2A)/3 + 1/5) = color(red)(30) xx 7/6`

`(color(red)(30) xx (2A)/3) + (color(red)(30) xx 1/5) = 210/6`

`(60A)/3 + 30/5 = 35`

`20A + 6 = 35`

Next, subtract `color(red)(6)` from each side of the equation to isolate the `A` term:

`20A + 6 - color(red)(6) = 35- color(red)(6)`

`20A + 0 = 29`

`20A = 29`

Now, divide each side of the equation by `color(red)(20)` to solve for `A` while keeping the equation balanced:

`(20A)/color(red)(20) = 29/color(red)(20)`

`(color(red)(cancel(color(black)(20)))A)/cancel(color(red)(20)) = 29/20`

`A = 29/20`