# How do you solve  8(2f - 2) = 7(3f + 2) ?

Apr 20, 2017

The final answer is $- 6 = f$.

#### Explanation:

$8 \left(2 f - 2\right) = 7 \left(3 f + 2\right)$

$\left(8 \cdot 2 f\right) + \left(8 \cdot - 2\right) = \left(7 \cdot 3 f\right) + \left(7 \cdot 2\right) \to$ Expand both sides by using the Distributive Property.

$16 f - 16 = 21 f + 14$

$\cancel{\textcolor{red}{16 f}} - 16 \cancel{\textcolor{red}{- 16 f}} = \cancel{21 f \textcolor{red}{- 16 f}} 5 f + 14 \to$ Subtract $16 f$ from both sides.

$\cancel{- 16 \textcolor{b l u e}{- 14}} - 30 = 5 f \cancel{\textcolor{b l u e}{+ 14}} \cancel{\textcolor{b l u e}{- 14}} \to$ Subtract $14$ from both sides.

$\cancel{- 30 \textcolor{g r e e n}{/ 5}} - 6 = \cancel{\textcolor{g r e e n}{5}} f \cancel{\textcolor{g r e e n}{/ 5}} \to$ Divide both sides by 5.

$- 6 = f \to$ Final answer!