# How do you solve for x: 6(x+1)=12(x-3)?

Feb 4, 2017

See the entire solution process below:

#### Explanation:

First, expand all the terms in exponents:

$\left(6 \times x\right) + \left(6 \times 1\right) = \left(12 \times x\right) - \left(12 \times 3\right)$

$6 x + 6 = 12 x - 36$

Next, subtract $\textcolor{red}{6 x}$ and add $\textcolor{b l u e}{36}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$6 x + 6 - \textcolor{red}{6 x} + \textcolor{b l u e}{36} = 12 x - 36 - \textcolor{red}{6 x} + \textcolor{b l u e}{36}$

$6 x - \textcolor{red}{6 x} + 6 + \textcolor{b l u e}{36} = 12 x - \textcolor{red}{6 x} - 36 + \textcolor{b l u e}{36}$

$0 + 42 = 6 x - 0$

$42 = 6 x$

Now, divide each side of the equation by $\textcolor{red}{6}$ to solve for $x$ while keeping the equation balanced:

$\frac{42}{\textcolor{red}{6}} = \frac{6 x}{\textcolor{red}{6}}$

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

$7 = x$

$x = 7$

Feb 4, 2017

$x = 7$

#### Explanation:

$6 \left(x + 1\right) = 12 \left(x - 3\right)$

$\therefore 6 x + 6 = 12 x - 36$

$\therefore 6 x - 12 x = - 36 - 6$

$\therefore - 6 x = - 42$

multiply both sides by$- 1$

$\therefore 6 x = 42$

$\therefore x = {\cancel{42}}^{7} / {\cancel{6}}^{1}$

$\therefore x = 7$

substitute $x = 7$

$\therefore 6 \left(7 + 1\right) = 12 \left(7 - 3\right)$

$\therefore 6 \times 8 = 12 \times 4$

$\therefore 48 = 48$