Question

How do you solve `\frac { n } { 2} + \frac { n - 1} { 2} = 1`?

Answer 1

See a solution process below:

Explanation:

First, add the fractions on the left side of the equation by adding the numerators over the common denominator:

`(n + (n - 1))/2 = 1`

`(1n + 1n - 1)/2 = 1`

`(2n - 1)/2 = 1`

Next, multiply each side of the equation by `color(red)(2)` to eliminate the fraction while keeping the equation balanced:

`color(red)(2) xx (2n - 1)/2 = color(red)(2) xx 1`

`cancel(color(red)(2)) xx (2n - 1)/color(red)(cancel(color(black)(2))) = 2`

`2n - 1 = 2`

Then, add `color(red)(1)` to each side of the equation to isolate the `n` term while keeping the equation balanced:

`2n - 1 + color(red)(1) = 2 + color(red)(1)`

`2n - 0 = 3`

`2n = 3`

Now, divide each side of the equation by `color(red)(2)` to solve the equation for `n` while keeping the equation balanced:

`(2n)/color(red)(2) = 3/color(red)(2)`

`(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = 3/2`

`n = 3/2`