Question

How do you solve `\frac { 17} { 8} = \frac { 14} { x - 2}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(8)(color(blue)(x - 2))` to eliminate the fraction making the equation easier to work with and to keep the equation balanced:

`color(red)(8)(color(blue)(x - 2)) xx 17/8 = color(red)(8)(color(blue)(x - 2)) xx 14/(x - 2)`

`cancel(color(red)(8))(color(blue)(x - 2)) xx 17/color(red)(cancel(color(black)(8))) = color(red)(8)cancel((color(blue)(x - 2))) xx 14/color(blue)(cancel(color(black)((x - 2))))`

`17(x - 2) = 8 xx 14`

`17(x - 2) = 112`

Next, expand the term on the left side of the equation:

`(17 xx x) - (17 xx 2) = 112`

`17x - 34 = 112`

Then, add `color(red)(34)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`17x - 34 + color(red)(34) = 112 + color(red)(34)`

`17x - 0 = 146`

`17x = 146`

Now, divide each side of the equation by `color(red)(17)` to solve for `x` while keeping the equation balanced:

`(17x)/color(red)(17) = 146/color(red)(17)`

`(color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17)) = 146/17`

`x = 146/17`