# How do you solve x/4-x/3=7/12-2?

Aug 1, 2016

Get rid of the fractions by multiplying the entire equation by $12$, then solve for x.

#### Explanation:

In order to solve this problem, we have to get rid of those pesky fractions. To do this, we're going to multiply both sides of the equation by the same number. This cancels out the fractions and makes solving this problem easier. We multiply the equation by $12$ so, for example, $\frac{x}{4}$ becomes $3 x$. This is what we're exactly doing:

$\frac{x}{4} \cdot 12 = \frac{x}{4} \cdot \frac{12}{1} = \frac{12 x}{4} = 3 x$

We can do this for the other two fractions:

$- \frac{x}{3} \cdot 12 = - \frac{x}{3} \cdot \frac{12}{1} = \frac{- 12 x}{3} = - 4 x$

$\frac{7}{12} \cdot 12 = \frac{7}{\cancel{12}} \cdot \frac{\cancel{12}}{1} = 7$

We also have to multiply $- 2$ by $12$ because we're multiplying both sides of the equation here:

$- 2 \cdot 12 = - 24$

Now, let's put all of the pieces together to get our simplified equation:

$12 \left(\frac{x}{4} - \frac{x}{3}\right) = \left(\frac{7}{12} - 2\right) 12$

$3 x - 4 x = 7 - 24$

Next, let's combine like terms. What this means is that two or more terms can be combined if the share the same variable or variables. In our case, we can combine $3 x$ and $- 4 x$ because the two terms both contain $x$:

$3 x - 4 x = - x$

Next, let's solve the right side of the equation by subtracting $24$ from $7$ to get $- 17$. We now have this:

$- x = - 17$

Finally, let's solve for $x$ and divide both sides of the equation by $- 1$:

$\frac{- x}{-} 1 = \frac{- 17}{-} 1$

$x = 17$