# How do you solve 19a - 3(a - 6) = 66 for a?

Jun 12, 2017

#### Answer:

See a solution process below:

#### Explanation:

First expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$19 a - \textcolor{red}{3} \left(a - 6\right) = 66$

$19 a - \left(\textcolor{red}{3} \cdot a\right) + \left(\textcolor{red}{3} \cdot 6\right) = 66$

$19 a - 3 a + 18 = 66$

Next, combine like terms:

$\left(19 - 3\right) a + 18 = 66$

$16 a + 18 = 66$

Then, subtract $\textcolor{red}{18}$ from each side of the equation to isolate the $a$ term while keeping the equation balanced:

$16 a + 18 - \textcolor{red}{18} = 66 - \textcolor{red}{18}$

$16 a + 0 = 48$

$16 a = 48$

Now, divide each side of the equation by $\textcolor{red}{16}$ to solve for $a$ while keeping the equation balanced:

$\frac{16 a}{\textcolor{red}{16}} = \frac{48}{\textcolor{red}{16}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{16}}} a}{\cancel{\textcolor{red}{16}}} = 3$

$a = 3$

Jun 12, 2017

#### Answer:

$a = 3$

#### Explanation:

$19 a - 3 \left(a - 6\right) = 66$

$19 a - 3 a + 18 = 66$

$19 a - 3 a \textcolor{red}{\cancel{\textcolor{b l a c k}{+ 18} - 18}} = 66 \textcolor{red}{- 18}$

$19 a - 3 a = 66 - 18$

$16 a = 66 - 18$

$16 a = 48$

color(red)(cancel(color(black)(16))) a color(red)(cancel(÷ 16)) = 48 ÷ 16

a = 48 ÷ 16

color(blue)(a = 3

We can substitute $a$ for $3$ to prove our answer.

$19 \times 3 - 3 \left(3 - 6\right) = 66$

$19 \times 3 - 3 \times - 3 = 66$

$57 - 3 \times - 3 = 66$

$57 - - 9 = 66$

$57 + 9 = 66$