Question

How do you solve `\frac { 3w + 7} { 6} + \frac { 2w + 2} { 3} = 10`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(6)` to eliminate the fractions while keeping the equation balanced. `color(red)(6)` is the lowest common denominator of the two fractions:

`color(red)(6)((3w + 7)/6 + (2w + 2)/3) = color(red)(6) xx 10`

`color(red)(6)((3w + 7)/6) + color(red)(6)((2w + 2)/3) = 60`

`cancel(color(red)(6))((3w + 7)/color(red)(cancel(color(black)(6)))) + cancel(color(red)(6))2((2w + 2)/color(red)(cancel(color(black)(3)))) = 60`

`3w + 7 + (2 xx 2w) + (2 xx 2) = 60`

`3w + 7 + 4w + 4 = 60`

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

`3w + 4w + 7 + 4 = 60`

`(3 + 4)w + (7 + 4) = 60`

`7w + 11 = 60`

Then, subtract `color(red)(11)` from each side of the equation to isolate the `w` term while keeping the equation balanced:

`7w + 11 - color(red)(11) = 60 - color(red)(11)`

`7w + 0 = 49`

`7w = 49`

Now, divide each side of the equation by `color(red)(7)` to solve for `w` while keeping the equation balanced:

`(7w)/color(red)(7) = 49/color(red)(7)`

`(color(red)(cancel(color(black)(7)))w)/cancel(color(red)(7)) = 7`

`w = 7`