Question

How do you solve `5/6(12p+4)=-13p+4`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply both sides of the equation by `color(red)(6)` to eliminate the fraction and keep the equation balanced:

`color(red)(6) xx 5/6(12p + 4) = color(red)(6)(-13p + 4)`

`cancel(color(red)(6)) xx 5/color(red)(cancel(color(black)(6)))(12p + 4) = color(red)(6)(-13p + 4)`

`5(12p + 4) = color(red)(6)(-13p + 4)`

`60p + 20 = -78p + 24`

Next add `color(red)(78p)` and subtract `color(blue)(20)` from each side of the equation to isolate the `p` terms while keeping the equation balanced:

`60p + 20 + color(red)(78p) - color(blue)(20) = -78p + 24 + color(red)(78p) - color(blue)(20)`

`60p + color(red)(78p) + 20 - color(blue)(20) = -78p + color(red)(78p) + 24 - color(blue)(20)`

`138p + 0 = 0 + 4`

`138p = 4`

Now, divide each side of the equation by `color(red)(138)` to solve for `p` while keeping the equation balanced:

`(138p)/color(red)(138) = 4/color(red)(138)`

`(color(red)(cancel(color(black)(138)))p)/cancel(color(red)(138)) = 2/69`

`p = 2/69`