How do you solve -67=-4n+3(1+6n) using the distributive property?

Jun 13, 2017

$n = - 5$

Explanation:

$- 67 = - 4 n + 3 \left(1 + 6 n\right)$

$- 67 = - 4 n + 3 + 18 n$

$- 67 \textcolor{red}{- 3} = - 4 n \textcolor{red}{\cancel{\textcolor{b l a c k}{+ 3} - 3}} + 18 n$

$- 70 = - 4 n + 18 n$

$- 70 = 14 n$

$- \frac{70}{14} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}} n}{\textcolor{red}{\cancel{14}}}$

$n = - \frac{70}{14}$

color(blue)(n = -5

Now we can substitute $n$ for $- 5$ to prove our answer.

$- 67 = - 4 \times - 5 + 3 \left(1 + 6 \times - 5\right)$

$- 67 = - 4 \times - 5 + 3 \left(1 + - 30\right)$

$- 67 = - 4 \times - 5 + 3 \times - 29$

$- 67 = 20 + 3 \times - 29$

$- 67 = 20 + - 87$

$- 67 = - 67$