Question

How do you solve `7p = 8( 6p + 5)`?

Answer 1

`p = -40/41`or `p = -0.976`

Explanation:

Distribute the `8` across the parentheses.

`7p = (8)(6p) + (8)(5)`

Now simplify the right side of the equation.

`7p = 48p + 40`

Start isolating the variable `p` by subtracting `48p` from both sides.

`7p - 48p = cancel(48p - 48p) + 40`

Simplify the left side of the equation.

`-41p = 40`

Divide `-41` from both sides to finish isolating the variable.

`(-41p)/-41 = 40/-41`

Simplify.

`p = -40/41`

The decimal equivalent rounded to the thousandths is `-0.976`.

Answer 2

See a solution process below:

Explanation:

First, expand the term in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`7p = color(red)(8)(6p + 5)`

`7p = (color(red)(8) xx 6p) + (color(red)(8) xx 5)`

`7p = 48p + 40`

Next, subtract `color(red)(48p)` from each side of the equation to isolate the `p` term while keeping the equation balanced:

`-color(red)(48p) + 7p = -color(red)(48p) + 48p + 40`

`(-color(red)(48) + 7)p = 0 + 40`

`-41p = 40`

Now, divide each side of the equation by `color(red)(-41)` to solve for `p` while keeping the equation balanced:

`(-41p)/color(red)(-41) = 40/color(red)(-41)`

`(color(red)(cancel(color(black)(-41)))p)/cancel(color(red)(-41)) = -40/41`

`p = -40/41`