How do you solve 3(x+7)= -2x-(3x+3)?

Feb 21, 2017

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on each side of the equation:

$\textcolor{red}{3} \left(x + 7\right) = - 2 x - \left(3 x + 3\right)$

$\left(\textcolor{red}{3} \times x\right) + \left(\textcolor{red}{3} \times 7\right) = - 2 x - 3 x - 3$

$3 x + 21 = \left(- 2 - 3\right) x - 3$

$3 x + 21 = - 5 x - 3$

Next, subtract $\textcolor{red}{21}$ and add $\textcolor{b l u e}{5 x}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$3 x + 21 - \textcolor{red}{21} + \textcolor{b l u e}{5 x} = - 5 x - 3 - \textcolor{red}{21} + \textcolor{b l u e}{5 x}$

$3 x + \textcolor{b l u e}{5 x} + 21 - \textcolor{red}{21} = - 5 x + \textcolor{b l u e}{5 x} - 3 - \textcolor{red}{21}$

$\left(3 + 5\right) x + 0 = 0 - 24$

$8 x = - 24$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $x$ while keeping the equation balanced:

$\frac{8 x}{\textcolor{red}{8}} = - \frac{24}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} x}{\cancel{\textcolor{red}{8}}} = - 3$

$x = - 3$