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

May 27, 2017

$p = - \frac{40}{41}$or $p = - 0.976$

#### Explanation:

Distribute the $8$ across the parentheses.

$7 p = \left(8\right) \left(6 p\right) + \left(8\right) \left(5\right)$

Now simplify the right side of the equation.

$7 p = 48 p + 40$

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

$7 p - 48 p = \cancel{48 p - 48 p} + 40$

Simplify the left side of the equation.

$- 41 p = 40$

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

$\frac{- 41 p}{-} 41 = \frac{40}{-} 41$

Simplify.

$p = - \frac{40}{41}$

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

May 27, 2017

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:

$7 p = \textcolor{red}{8} \left(6 p + 5\right)$

$7 p = \left(\textcolor{red}{8} \times 6 p\right) + \left(\textcolor{red}{8} \times 5\right)$

$7 p = 48 p + 40$

Next, subtract $\textcolor{red}{48 p}$ from each side of the equation to isolate the $p$ term while keeping the equation balanced:

$- \textcolor{red}{48 p} + 7 p = - \textcolor{red}{48 p} + 48 p + 40$

$\left(- \textcolor{red}{48} + 7\right) p = 0 + 40$

$- 41 p = 40$

Now, divide each side of the equation by $\textcolor{red}{- 41}$ to solve for $p$ while keeping the equation balanced:

$\frac{- 41 p}{\textcolor{red}{- 41}} = \frac{40}{\textcolor{red}{- 41}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 41}}} p}{\cancel{\textcolor{red}{- 41}}} = - \frac{40}{41}$

$p = - \frac{40}{41}$