Question

How do you solve `\frac { x + 3} { 2} + \frac { 2x } { 7} = 7`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(14)` to eliminate the fractions while keeping the equation balanced. `color(red)(14)` is the Least Common Denominator for the two fractions:

`color(red)(14)((x + 3)/2 + (2x)/7) = color(red)(14) xx 7`

`(color(red)(14) xx (x + 3)/2) + (color(red)(14) xx (2x)/7) = 98`

`(cancel(color(red)(14))7 xx (x + 3)/color(red)(cancel(color(black)(2)))) + (cancel(color(red)(14))2 xx (2x)/color(red)(cancel(color(black)(7)))) = 98`

`7(x + 3) + 4x = 98`

`(7 xx x) + (7 xx 3) + 4x = 98`

`7x + 21 + 4x = 98`

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

`7x + 4x + 21 = 98`

`(7 + 4)x + 21 = 98`

`11x + 21 = 98`

Then, subtract `color(red)(21)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`11x + 21 - color(red)(21) = 98 - color(red)(21)`

`11x + 0 = 77`

`11x = 77`

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

`(11x)/color(red)(11) = 77/color(red)(11)`

`(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 7`

`x = 7`