Question

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

Answer 1

You cross-multiply, using `A/B=C/DharrAxxD=BxxC`

Explanation:

`->2*(x+1)=3*6`

`->2x+2=18->2x=16->x=8`

Check:
`2/3=6/(8+1)`

Answer 2

See the entire solution process below:

Explanation:

First, multiply each side of the equation by the common denominator of the two fractions which is `color(red)(3)color(blue)((x + 1))` to eliminate the fractions while keeping the equation balanced:

`color(red)(3)color(blue)((x + 1)) xx 2/3 = color(red)(3)color(blue)((x + 1)) xx 6/(x + 1)`

`cancel(color(red)(3))color(blue)((x + 1)) xx 2/color(red)(cancel(color(black)(3))) = color(red)(3)cancel(color(blue)((x + 1))) xx 6/color(blue)(cancel(color(black)(x + 1)))`

`2(x + 1) = 18`

Now, divide each side of the equation by `color(red)(2)` to eliminate the term outside the parenthesis while keeping the equation balanced:

`(2(x + 1))/color(red)(2) = 18/color(red)(2)`

`(color(red)(cancel(color(black)(2)))(x + 1))/cancel(color(red)(2)) = 9`

`x + 1 = 9`

Now, subtract `color(red)(1)` from each side of the equation to solve for `x`:

`x + 1 - color(red)(1) = 9 - color(red)(1)`

`x + 0 = 8`

`x = 8`