# How do you solve 3a+13=9a-8?

Dec 21, 2016

$a = \frac{7}{2}$

#### Explanation:

First, isolate the $a$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$3 a + 13 - \textcolor{red}{3 a + 8} = 9 a - 8 - \textcolor{red}{3 a + 8}$

$3 a - 3 a + 13 + 8 = 9 a - 3 a - 8 + 8$

$0 + 13 + 8 = 9 a - 3 a - 0$

$13 + 8 = 9 a - 3 a$

Next, we can combine like terms:

$21 = \left(9 - 3\right) a$

$21 = 6 a$

Now, solve for $a$ while keeping the equation balanced:

$\frac{21}{\textcolor{red}{6}} = \frac{6 a}{\textcolor{red}{6}}$

$\frac{3 \times 7}{3 \times 2} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} a}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}}$

$\frac{3}{3} \times \frac{7}{2} = a$

$1 \times \frac{7}{2} = a$

$\frac{7}{2} = a$