# How do you solve -3(x-1)+9=15?

Dec 26, 2016

$x = - 1$

#### Explanation:

The first step is to expand the terms in parenthesis by multiplying each term within the parenthesis by $\textcolor{red}{- 3}$ being careful to ensure the sign of the product is correct:

$\left(\textcolor{red}{- 3} \cdot x\right) + \left(\textcolor{red}{- 3} \cdot - 1\right) + 9 = 15$

$- 3 x + 3 + 9 = 15$

Next we can combine the like terms on the left side of the equation:

$- 3 x + \left(3 + 9\right) = 15$

$- 3 x + 12 = 15$

Then, we can subtract $\textcolor{b l u e}{12}$ from each side of the equation to isolate the $x$ term and keep the equation balanced:

$- 3 x + 12 - \textcolor{b l u e}{12} = 15 - \textcolor{b l u e}{12}$

$- 3 x + 0 = 3$

$- 3 x = 3$

Now, we can divide each side of the equation by $\textcolor{g r e e n}{- 3}$ to solve for $x$ and keep the equation balanced:

$\frac{- 3 x}{\textcolor{g r e e n}{- 3}} = \frac{3}{\textcolor{g r e e n}{- 3}}$

$\frac{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{- 3}}} x}{\cancel{\textcolor{g r e e n}{- 3}}} = - 1$

$x = - 1$