Math Snap

STEP 1

Assumptions1. The equation is $-\frac{5}{6} y-\frac{1}{5} y=\frac{4}{3}-\frac{1}{5}$
. We need to isolate the variable $y$.

STEP 2

First, we need to combine like terms on both sides of the equation. On the left side, we have $-\frac{5}{6} y$ and $-\frac{1}{5} y$. On the right side, we have $\frac{4}{}$ and $-\frac{1}{5}$.

STEP 3

To combine $-\frac{5}{6} y$ and $-\frac{1}{5} y$, we need to find a common denominator. The least common multiple of6 and5 is30.
$$-\frac{5}{6} y-\frac{1}{5} y = -\frac{25}{30} y - \frac{6}{30} y$$

STEP 4

Now, combine the terms on the left side of the equation.
$$-\frac{25}{30} y - \frac{6}{30} y = -\frac{31}{30} y$$

STEP 5

Similarly, combine the terms on the right side of the equation.
$$\frac{4}{3} - \frac{1}{5} = \frac{20}{15} - \frac{3}{15} = \frac{17}{15}$$

STEP 6

So, the equation becomes$$-\frac{31}{30} y = \frac{17}{15}$$

STEP 7

To isolate $y$, divide both sides of the equation by $-\frac{31}{30}$.
$$y = \frac{\frac{17}{15}}{-\frac{31}{30}}$$

STEP 8

This simplifies to$$y = \frac{17}{15} \times \frac{-30}{31}$$

implify the expression to get the final answer.
$$y = \frac{-17}{31}$$So, $y = -\frac{17}{31}$ is the solution to the equation.