# How do you solve (x-3/12)+2x-1/15= (3x+1/4)?

Jun 17, 2016

There is no solution to this equation.

#### Explanation:

The first thing we probably notice in this equation is that there are fractions. Luckily, because it is an equation, we can get rid of the fractions and work with only whole numbers.

The brackets are not necessary, leave them out.

$x - \frac{3}{12} + 2 x - \frac{1}{15} = 3 x + \frac{1}{4}$

The LCM of the denominators would be 60. (divisible by 4, 12, 15)
Instead of converting everything to a common denominator, MULTIPLY every term by 60. This will allow us to cancel the denominators.

$\textcolor{b l u e}{60 \times} x - \textcolor{b l u e}{60 \times} \frac{3}{12} + \textcolor{b l u e}{60 \times} 2 x - \textcolor{b l u e}{60 \times} \frac{1}{15} = \textcolor{b l u e}{60 \times} 3 x + \textcolor{b l u e}{60 \times} \frac{1}{4}$

$60 x - \textcolor{b l u e}{{\cancel{60}}^{5} \times} \frac{3}{\cancel{12}} + 120 x - \textcolor{b l u e}{{\cancel{60}}^{4} \times} \frac{1}{\cancel{15}} = 180 x + \textcolor{b l u e}{{\cancel{60}}^{15} \times} \frac{1}{\cancel{4}}$

$60 x - 15 + 120 x - 4 = 180 x + 15$
$180 x - 19 = 180 x + 15$
$180 x - 180 x = 15 + 19$
$0 = 34$

There is no $x -$term left, but we have ended up with a false statement.
This tells us that there is no solution to this equation.

(If we had ended up with 0=0, then it would have true for any value of $x$.)