# How do you solve 3(x-7) = 6(x-10)?

Jun 29, 2018

$x = 13$

#### Explanation:

$3 \left(x - 7\right) = 6 \left(x - 10\right)$

Use the distributive property (shown below) to simplify each side:

Following this image, we know that:
$\textcolor{b l u e}{3 \left(x - 7\right) = \left(3 \cdot x\right) + \left(3 \cdot - 7\right) = 3 x - 21}$
and
$\textcolor{b l u e}{6 \left(x - 10\right) = \left(6 \cdot x\right) + \left(6 \cdot - 10\right) = 6 x - 60}$

Put them back into the equation:
$3 x - 21 = 6 x - 60$

Subtract $\textcolor{b l u e}{6} x$ from both sides:
$3 x - 21 \quad \textcolor{b l u e}{- \quad 6 x} = 6 x - 60 \quad \textcolor{b l u e}{- \quad 6 x}$

$- 3 x - 21 = - 60$

Add $\textcolor{b l u e}{21}$ on both sides:
$- 3 x - 21 \quad \textcolor{b l u e}{+ \quad 21} = - 60 \quad \textcolor{b l u e}{+ \quad 21}$

$- 3 x = - 39$

Divide both sides by $\textcolor{b l u e}{- 3}$:
$\frac{- 3 x}{\textcolor{b l u e}{- 3}} = \frac{- 39}{\textcolor{b l u e}{- 3}}$

Therefore,
$x = 13$

Hope this helps!

Aug 5, 2018

$x = 13$

#### Explanation:

We can divide both sides by $3$ to get

$x - 7 = 2 \left(x - 10\right)$

Next, we can distribute the $2$ on the right to get

$x - 7 = 2 x - 20$

Next, we can add $7$ to both sides to get

$x = 2 x - 13$

To get our constants on one side, we can subtract $2 x$ from both sides to get

$- x = - 13$

Lastly, we can divide both sides by $- 1$ to get

$x = 13$

Hope this helps!