# How do you solve 2/3x+3=x-2?

Mar 11, 2018

$x = 15$

#### Explanation:

First let's get all like-terms on the same sides.
To do so, we can subtract 3 from both sides and subtract $x$ from both sides as well.

$\frac{2}{3} x + 3 - 3 - x = x - 2 - 3 - x$

Simplify:
$\frac{2}{3} x - x = - 2 - 3$

Now we can combine like-terms:
$- \frac{1}{3} x = - 5$

In order to isolate $x$, multiply by -3 on both sides:
$- 3 \cdot - \frac{1}{3} x = - 5 \cdot - 3$

Simplify:
$x = 15$

Mar 11, 2018

$x = 15$

#### Explanation:

So the first thing you would want to do is to move the $\frac{2}{3} x$ over to the right side of the equation, making it $- \frac{2}{3} x$.

Subtract $x - \frac{2}{3} x$. Since the is no coefficient, $x$ means #3/3x, so

$x - \frac{2}{3} x = \frac{1}{3} x$

Now move the whole number $- 2$ to the left side, making it

$3 + 2 = 5$

Multiply both sides by $3$ to get $x$ alone.

$x = 15$