Solve for j (-4j-(-5))/-7=13

$\frac{- 4 j - (- 5)}{- 7} = 13$

Step 1

Multiply both sides by $- 7$ .

$\frac{- 4 j - (- 5)}{- 7} \cdot - 7 = 13 \cdot - 7$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{- 4 j - (- 5)}{- 7} \cdot - 7$ .

Multiply $- 1$ by $- 5$ .

$\frac{- 4 j + 5}{- 7} \cdot - 7 = 13 \cdot - 7$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7$ .

$\frac{- 4 j + 5}{7 (- 1)} \cdot - 7 = 13 \cdot - 7$

Factor $7$ out of $- 7$ .

$\frac{- 4 j + 5}{7 \cdot - 1} \cdot (7 \cdot - 1) = 13 \cdot - 7$

Cancel the common factor.

$\frac{- 4 j + 5}{7 \cdot - 1} \cdot (7 \cdot - 1) = 13 \cdot - 7$

Rewrite the expression.

$\frac{- 4 j + 5}{- 1} \cdot - 1 = 13 \cdot - 7$

Combine $\frac{- 4 j + 5}{- 1}$ and $- 1$ .

$\frac{(- 4 j + 5) \cdot - 1}{- 1} = 13 \cdot - 7$

Simplify the expression.

Move the negative one from the denominator of $\frac{(- 4 j + 5) \cdot - 1}{- 1}$ .

$- 1 \cdot ((- 4 j + 5) \cdot - 1) = 13 \cdot - 7$

Rewrite $- 1 \cdot ((- 4 j + 5) \cdot - 1)$ as $- ((- 4 j + 5) \cdot - 1)$ .

$- ((- 4 j + 5) \cdot - 1) = 13 \cdot - 7$

Apply the distributive property.

$- (- 4 j \cdot - 1 + 5 \cdot - 1) = 13 \cdot - 7$

Multiply.

Multiply $- 1$ by $- 4$ .

$- (4 j + 5 \cdot - 1) = 13 \cdot - 7$

Multiply $5$ by $- 1$ .

$- (4 j - 5) = 13 \cdot - 7$

Apply the distributive property.

$- (4 j) - - 5 = 13 \cdot - 7$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 j - - 5 = 13 \cdot - 7$

Multiply $- 1$ by $- 5$ .

$- 4 j + 5 = 13 \cdot - 7$

Simplify the right side.

Multiply $13$ by $- 7$ .

$- 4 j + 5 = - 91$

Step 3

Solve for $j$ .

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

Subtract $5$ from both sides of the equation.

$- 4 j = - 91 - 5$

Subtract $5$ from $- 91$ .

$- 4 j = - 96$

Divide each term in $- 4 j = - 96$ by $- 4$ and simplify.

Divide each term in $- 4 j = - 96$ by $- 4$ .

$\frac{- 4 j}{- 4} = \frac{- 96}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 j}{- 4} = \frac{- 96}{- 4}$

Divide $j$ by $1$ .

$j = \frac{- 96}{- 4}$

Simplify the right side.

Divide $- 96$ by $- 4$ .

$j = 24$

Solve for j (-4j-(-5))/-7=13

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