# How do you solve 9(2 - 3x) - 29 = 8x + 23 - x?

Jan 8, 2018

See a solution process below:

#### Explanation:

First rewrite the expression as:

$9 \left(2 - 3 x\right) - 29 = 8 x - x + 23$

Next, expand the term in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{9} \left(2 - 3 x\right) - 29 = 8 x - x + 23$

$\left(\textcolor{red}{9} \times 2\right) - \left(\textcolor{red}{9} \times 3 x\right) - 29 = 8 x - x + 23$

$18 - 27 x - 29 = 8 x - x + 23$

Then, group and combine like terms on each side of the equation:

$18 - 29 - 27 x = 8 x - x + 23$

$- 11 - 27 x = \left(8 - 1\right) x + 23$

$- 11 - 27 x = 7 x + 23$

Next, add $\textcolor{red}{27 x}$ and subtract $\textcolor{b l u e}{23}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- 11 - \textcolor{b l u e}{23} - 27 x + \textcolor{red}{27 x} = 7 x + \textcolor{red}{27 x} + 23 - \textcolor{b l u e}{23}$

$- 34 - 0 = \left(7 + \textcolor{red}{27}\right) x + 0$

$- 34 = 34 x$

Now, divide each side of the equation by $\textcolor{red}{34}$ to solve for $x$ while keeping the equation balanced:

$- \frac{34}{\textcolor{red}{34}} = \frac{34 x}{\textcolor{red}{34}}$

$- 1 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{34}}} x}{\cancel{\textcolor{red}{34}}}$

$- 1 = x$

$x = - 1$

Jan 8, 2018

$x = - 1$

#### Explanation:

Ok, so there are a few steps to this problem. First we need to combine like terms. Then we will subtract the lowest term from both sides. Let me explain:

We begin with the problem

$9 \left(2 - 3 x\right) - 29 = 8 x - \left(x - 23\right)$

We need o get rid of the parentheses. To do this we just multiply everything in the parentheses by whats outside of them

$18 - 27 x - 29 = 8 x - x + 23$

Now we need to combine like terms

$- 27 x - 11 = 7 x + 23$

Ok, finally, we need to get $x$ on one side with (hopefully) the answer on the other

(Subtract $7 x$)
$- 27 x - 11 - 7 x = \cancel{7 x} + 23 \cancel{- 7 x}$

$- 34 x - 11 = 23$

(Add $11$)
$- 34 x \cancel{- 11} + \cancel{11} = 23 + 11$

$- 34 x = 34$

(Divide by $- 34$)
$\frac{\cancel{- 34 x}}{\cancel{- 34}} = \frac{34}{-} 34$

$x = - 1$

Hope this helped!
~Chandler Dowd