Question

How do you solve `\frac { 7} { 6} = \frac { 2} { p - 2}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(6)(color(blue)(p - 2))` to eliminate the fractions while keeping the equation balanced. `color(red)(6)(color(blue)(p - 2))` is the Lowest Common Denominator of the two fractions:

`color(red)(6)(color(blue)(p - 2)) xx 7/6 = color(red)(6)(color(blue)(p - 2)) xx 2/(p - 2)`

`cancel(color(red)(6))(color(blue)(p - 2)) xx 7/color(red)(cancel(color(black)(6))) = color(red)(6)cancel((color(blue)(p - 2))) xx 2/color(blue)(cancel(color(black)((p - 2)))`

`7(p - 2) = 12`

`(7 xx p) - (7 xx 2) = 12`

`7p - 14 = 12`

Next, add `color(red)(14)` to each side of the equation to isolate the `p` term while keeping the equation balanced:

`7p - 14 + color(red)(14) = 12 + color(red)(14)`

`7p - 0 = 26`

`7p = 26`

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

`(7p)/color(red)(7) = 26/color(red)(7)`

`(color(red)(cancel(color(black)(7)))p)/cancel(color(red)(7)) = 26/7`

`p = 26/7`