Solve for y 6=(-5+y)/-7

$6 = \frac{- 5 + y}{- 7}$

Step 1

Rewrite the equation as $\frac{- 5 + y}{- 7} = 6$ .

$\frac{- 5 + y}{- 7} = 6$

Step 2

Multiply both sides of the equation by $- 7$ .

$- 7 \frac{- 5 + y}{- 7} = - 7 \cdot 6$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 7 \frac{- 5 + y}{- 7}$ .

Cancel the common factor of $7$ .

Factor $7$ out of $- 7$ .

$7 (- 1) \frac{- 5 + y}{- 7} = - 7 \cdot 6$

Factor $7$ out of $- 7$ .

$7 \cdot - 1 \frac{- 5 + y}{7 \cdot - 1} = - 7 \cdot 6$

Cancel the common factor.

$7 \cdot - 1 \frac{- 5 + y}{7 \cdot - 1} = - 7 \cdot 6$

Rewrite the expression.

$- \frac{- 5 + y}{- 1} = - 7 \cdot 6$

Simplify the expression.

Move the negative one from the denominator of $\frac{- 5 + y}{- 1}$ .

$- (- 1 \cdot (- 5 + y)) = - 7 \cdot 6$

Rewrite $- 1 \cdot (- 5 + y)$ as $- (- 5 + y)$ .

$- - (- 5 + y) = - 7 \cdot 6$

Apply the distributive property.

$- (- - 5 - y) = - 7 \cdot 6$

Multiply $- 1$ by $- 5$ .

$- (5 - y) = - 7 \cdot 6$

Apply the distributive property.

$- 1 \cdot 5 - - y = - 7 \cdot 6$

Multiply $- 1$ by $5$ .

$- 5 - - y = - 7 \cdot 6$

Multiply $- - y$ .

Multiply $- 1$ by $- 1$ .

$- 5 + 1 y = - 7 \cdot 6$

Multiply $y$ by $1$ .

$- 5 + y = - 7 \cdot 6$

Simplify the right side.

Multiply $- 7$ by $6$ .

$- 5 + y = - 42$

Step 4

Move all terms not containing $y$ to the right side of the equation.

Add $5$ to both sides of the equation.

$y = - 42 + 5$

Add $- 42$ and $5$ .

$y = - 37$

Solve for y 6=(-5+y)/-7

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