# How do you solve -\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7}?

Mar 1, 2017

$y = \frac{3}{28}$

#### Explanation:

$- \setminus \frac{1}{2} = \setminus \frac{2}{3} y - \setminus \frac{4}{7}$

As soon as you have an EQUATION with fractions, you can get rid of the denominators immediately.

Multiply each term by the LCM of the denominators.
In this case it is $42$

$\frac{\textcolor{b l u e}{42 \times} - 1}{2} = \frac{\textcolor{b l u e}{42 \times} 2}{3} y - \frac{\textcolor{b l u e}{42 \times} 4}{7} \text{ } \leftarrow$ cancel

$\frac{{\cancel{42}}^{21} \times - 1}{\cancel{2}} = \frac{{\cancel{42}}^{14} \times 2}{\cancel{3}} y - \frac{{\cancel{42}}^{6} \times 4}{\cancel{7}}$

$- 21 = 28 y - 24 \text{ } \leftarrow$ add 24 to both sides

$- 21 + 24 = 28 y - 24 + 24$

$3 = 28 y$

$\frac{3}{28} = y$