# How do you solve 3(x-18)=5(x-12)?

Mar 25, 2018

$x = 3$

#### Explanation:

$3 \left(x - 18\right) = 5 \left(x - 12\right)$

Let's expand the equation by doing the multiplication
$3 x - 54 = 5 x - 60$

Now if we add to both sides $54$, this number will be moved from the left to the right
$\textcolor{red}{+ 54} + 3 x - 54 = 5 x - 60 \textcolor{red}{+ 54}$

$3 x = 5 x - 60 + 54$

Same thing can be applied with $5 x$
$\textcolor{red}{- 5 x} + 3 x = 5 x - 60 + 54 \textcolor{red}{- 5 x}$

$3 x - 5 x = - 60 + 54$

And what we have to do now is just the sum of the similiar terms
$- 2 x = - 6$

Multiplying both term by $- 1$, we gain an equation with positive $x$
$\textcolor{b l u e}{- 1} \cdot - 2 x = - 6 \cdot \textcolor{b l u e}{- 1}$

$2 x = 6$

And to finally get the result we can divide both term by $2$
$\frac{2}{\setminus} \textcolor{b l u e}{2} x = \frac{6}{\textcolor{b l u e}{2}}$

x=3

To check whether the result it's right, just plug in the value in the initial equation. If the left and right quantity are the same we did a good job.