# How do you solve 4(x-9)-3(-x+2)=14?

Oct 23, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to handle the signs for each term correctly:

$\textcolor{red}{4} \left(x - 9\right) - \textcolor{b l u e}{3} \left(- x + 2\right) = 14$

$\left(\textcolor{red}{4} \times x\right) - \left(\textcolor{red}{4} \times 9\right) - \left(\textcolor{b l u e}{3} \times - x\right) - \left(\textcolor{b l u e}{3} \times 2\right) = 14$

$4 x - 36 - \left(- 3 x\right) - 6 = 14$

$4 x - 36 + 3 x - 6 = 14$

Next, group and combine like terms:

$4 x + 3 x - 36 - 6 = 14$

$\left(4 + 3\right) x + \left(- 36 - 6\right) = 14$

$7 x + \left(- 42\right) = 14$

$7 x - 42 = 14$

Then, add $\textcolor{red}{42}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$7 x - 42 + \textcolor{red}{42} = 14 + \textcolor{red}{42}$

$7 x - 0 = 56$

$7 x = 56$

Now, divide each side of the equation by $\textcolor{red}{7}$ to solve for $x$ while keeping the equation balanced:

$\frac{7 x}{\textcolor{red}{7}} = \frac{56}{\textcolor{red}{7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}{\cancel{\textcolor{red}{7}}} = 8$

$x = 8$