Solve for w -61=8-1/3(12w+42)-w

$- 61 = 8 - \frac{1}{3} (12 w + 42) - w$

Step 1

Rewrite the equation as $8 - \frac{1}{3} \cdot (12 w + 42) - w = - 61$ .

$8 - \frac{1}{3} \cdot (12 w + 42) - w = - 61$

Step 2

Simplify $8 - \frac{1}{3} \cdot (12 w + 42) - w$ .

Simplify each term.

Apply the distributive property.

$8 - \frac{1}{3} (12 w) - \frac{1}{3} \cdot 42 - w = - 61$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$8 + \frac{- 1}{3} (12 w) - \frac{1}{3} \cdot 42 - w = - 61$

Factor $3$ out of $12 w$ .

$8 + \frac{- 1}{3} (3 (4 w)) - \frac{1}{3} \cdot 42 - w = - 61$

Cancel the common factor.

$8 + \frac{- 1}{3} (3 (4 w)) - \frac{1}{3} \cdot 42 - w = - 61$

Rewrite the expression.

$8 - 1 (4 w) - \frac{1}{3} \cdot 42 - w = - 61$

Multiply $4$ by $- 1$ .

$8 - 4 w - \frac{1}{3} \cdot 42 - w = - 61$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$8 - 4 w + \frac{- 1}{3} \cdot 42 - w = - 61$

Factor $3$ out of $42$ .

$8 - 4 w + \frac{- 1}{3} \cdot (3 (14)) - w = - 61$

Cancel the common factor.

$8 - 4 w + \frac{- 1}{3} \cdot (3 \cdot 14) - w = - 61$

Rewrite the expression.

$8 - 4 w - 1 \cdot 14 - w = - 61$

Multiply $- 1$ by $14$ .

$8 - 4 w - 14 - w = - 61$

Simplify by adding terms.

Subtract $14$ from $8$ .

$- 4 w - 6 - w = - 61$

Subtract $w$ from $- 4 w$ .

$- 5 w - 6 = - 61$

Step 3

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

Add $6$ to both sides of the equation.

$- 5 w = - 61 + 6$

Add $- 61$ and $6$ .

$- 5 w = - 55$

Step 4

Divide each term in $- 5 w = - 55$ by $- 5$ and simplify.

Divide each term in $- 5 w = - 55$ by $- 5$ .

$\frac{- 5 w}{- 5} = \frac{- 55}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 w}{- 5} = \frac{- 55}{- 5}$

Divide $w$ by $1$ .

$w = \frac{- 55}{- 5}$

Simplify the right side.

Divide $- 55$ by $- 5$ .

$w = 11$

Solve for w -61=8-1/3(12w+42)-w

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