# How do you solve -\frac { 2x - 6} { 3} = \frac { x } { 5} + 2?

Jun 23, 2017

x = 0

#### Explanation:

Multiply all the terms by 15 the least common multiple.

$15 \times - \frac{2 x - 6}{3} = 15 \times \left(\frac{x}{5} + 2\right)$ This gives

$- 10 x + 30 = 3 x + 30$ subtract 30 from both sides

$- 10 x + 30 - 30 = 3 x + 30 - 30$ the result is

$- 10 x = 3 x$ add 10x to both sides

$- 10 x + 10 x = 3 x + 10 x$ which equals

$0 = 13 x$ divide both sides by 13

$\frac{0}{13} = \frac{13 x}{13}$ the answer is

$0 = x$

Jun 23, 2017

Answer: $x = 0$

#### Explanation:

Solve $- \frac{2 x - 6}{3} = \frac{x}{5} + 2$ for $x$.

We can start by getting rid of the fractions by multiplying everything by the least common multiple (lcm) of the denominators ($3$, $5$, and $1$), which is $15$.

So, we get:
$15 \left(- \frac{2 x - 6}{3} = \frac{x}{5} + 2\right)$

$- 5 \left(2 x - 6\right) = 3 x + 30$

Simplifying, we get:
$- 10 x + 30 = 3 x + 30$

Subtracting $30$ from both sides and adding $10 x$ to both sides, we get:
$13 x = 0$

Dividing both sides by $13$, we get our answer:
$x = 0$