# How do you simplify \frac{1}{3}x+2=\frac{1}{2}x-1?

Jul 7, 2018

Multiply by 6

$2 x + 12 = 3 x - 6$

Subtract $2 x$

$12 = x - 6$

$x = 18$

Jul 7, 2018

$x = 18$

#### Explanation:

Given: $\frac{1}{3} x + 2 = \frac{1}{2} x - 1$.

Subtract $2$ from both sides.

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

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

Multiply both sides by the greatest common factor $\left(\boldsymbol{G C F}\right)$ of the denominators, which is $2 \cdot 3 = 6$.

$6 \left(\frac{1}{3} x\right) = 6 \left(\frac{1}{2} x - 3\right)$

$2 x = 3 x - 18$

Subtract $3 x$ from both sides.

$2 x - 3 x = - 18$

$- x = - 18$

Multiplying both sides by $- 1$ yields:

$\therefore x = 18$

Jul 7, 2018

$x = 18$

#### Explanation:

We can get rid of the fractions by multiplying by the LCM of the denominators, which happens to be $6$.

We now have

$2 x + 12 = 3 x - 6$

Let's subtract $12$ from both sides to get

$2 x = 3 x - 18$

Next, we can subtract $3 x$ from both sides. We now have

$- x = - 18$

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

$x = 18$

Hope this helps!