# How do you solve -4(x-8)+(-x-3)=4?

Mar 24, 2017

$x = 5$

#### Explanation:

Lets simplify this equation first by distributing the $- 4$ to $\left(x - 8\right)$

$- 4 \left(x - 8\right) \to - 4 x + 32$

Now lets combine like terms:
$\textcolor{b l u e}{- 4 x} + \textcolor{red}{32} \textcolor{b l u e}{- x} \textcolor{red}{- 3} = \textcolor{red}{4} \to \textcolor{b l u e}{- 5 x} + \textcolor{red}{29} = \textcolor{red}{4}$

Now we'll isolate the $x$ by first subtracting 29 from both sides:

$\textcolor{b l u e}{- 5 x} + \textcolor{red}{\cancel{29 - 29}} = \textcolor{red}{4 - 29}$

$\textcolor{b l u e}{- 5 x} = \textcolor{red}{- 25}$

Then divide $5$ on both sides:
$\textcolor{b l u e}{\cancel{- \frac{5}{5} x}} = \textcolor{red}{- \frac{25}{5}}$

$\textcolor{b l u e}{x} = \textcolor{red}{5}$

We can verify the solution but substituting $5$ for $x$ in the original equation.

$- 4 \left(\left(\textcolor{red}{5}\right) - 8\right) - \left(\textcolor{red}{5}\right) - 3 = 4$

$- 4 \left(- 3\right) - \left(\textcolor{red}{5}\right) - 3 = 4$

$12 - \left(\textcolor{red}{5}\right) - 3 = 4$

$7 - 3 = 4$

$4 = 4$

Mar 24, 2017

$x = 5$

#### Explanation:

Solve:

$- 4 \left(x - 8\right) + \left(- x - 3\right) = 4$

Expand.

$- 4 x + 32 + \left(- x - 3\right) = 4$

Remove the parentheses.

$- 4 x + 32 - x - 3 = 4$

Gather like terms.

$- 4 x - x + 32 - 3 = 4$

Simplify.

$- 5 x + 29 = 4$

Subtract $29$ from both sides.

$- 5 x + \cancel{29} - \cancel{29} = 4 - 29$

$- 5 x = - 25$

Divide both sides by $- 5$.

$\frac{\cancel{- 5} x}{\cancel{- 5}} = {\cancel{- 25}}^{5} / {\cancel{- 5}}^{1}$

$x = 5$