# How do you solve -27x - 67= 122- 24x?

May 25, 2018

$x = - 63$

#### Explanation:

$- 27 x - 67 = 122 - 24 x$

First, you want to remove the variable of the lowest value so that way you can solve this as a two-step equation. In this case, the variable with the lowest value is $- 27 x$. In order to get rid of it, we'll add $27 x$ to cancel out the $- 27$. Because you add to one side, you must add to the other side to become equal. So, $27 x - 24 x = 3 x$ on the right side. Your equation should now look like this:

$- 67 = 122 + 3 x$

Now, subtract $122$ from both sides to cancel out $122$ in order to isolate for $x$. $- 67 - 122 = - 189$. Recall that two numbers of the same sign technically add up. Your equation should now look like this:

$- 189 = 3 x$

Now, divide by $3$ in order to isolate for $x$. $\frac{3}{3}$ = $1$, and $- \frac{189}{3}$ = $- 63$, so this will be the value of your variable.

$x = - 63$

To verify that $x$ really is $- 63$, we'll plug it back into the equation. Replace $x$ with the value $- 63$.

$- 27 x - 67 = 122 - 24 x$
$- 27 \left(- 63\right) - 67 = 122 - 24 \left(- 63\right)$
$1701 - 67 = 122 + 1512$
$1634 = 1634$

$x = - 63$