Solve for w 30w-(-w+6)+(-5w+4)=-(5w+6)+(-8+3w)

$30 w - (- w + 6) + (- 5 w + 4) = - (5 w + 6) + (- 8 + 3 w)$

Step 1

Simplify $30 w - (- w + 6) - 5 w + 4$ .

Simplify each term.

Apply the distributive property.

$30 w - - w - 1 \cdot 6 - 5 w + 4 = - (5 w + 6) - 8 + 3 w$

Multiply $- - w$ .

Multiply $- 1$ by $- 1$ .

$30 w + 1 w - 1 \cdot 6 - 5 w + 4 = - (5 w + 6) - 8 + 3 w$

Multiply $w$ by $1$ .

$30 w + w - 1 \cdot 6 - 5 w + 4 = - (5 w + 6) - 8 + 3 w$

Multiply $- 1$ by $6$ .

$30 w + w - 6 - 5 w + 4 = - (5 w + 6) - 8 + 3 w$

Simplify by adding terms.

Add $30 w$ and $w$ .

$31 w - 6 - 5 w + 4 = - (5 w + 6) - 8 + 3 w$

Subtract $5 w$ from $31 w$ .

$26 w - 6 + 4 = - (5 w + 6) - 8 + 3 w$

Add $- 6$ and $4$ .

$26 w - 2 = - (5 w + 6) - 8 + 3 w$

Step 2

Simplify $- (5 w + 6) - 8 + 3 w$ .

Simplify each term.

Apply the distributive property.

$26 w - 2 = - (5 w) - 1 \cdot 6 - 8 + 3 w$

Multiply $5$ by $- 1$ .

$26 w - 2 = - 5 w - 1 \cdot 6 - 8 + 3 w$

Multiply $- 1$ by $6$ .

$26 w - 2 = - 5 w - 6 - 8 + 3 w$

Simplify by adding terms.

Add $- 5 w$ and $3 w$ .

$26 w - 2 = - 2 w - 6 - 8$

Subtract $8$ from $- 6$ .

$26 w - 2 = - 2 w - 14$

Step 3

Move all terms containing $w$ to the left side of the equation.

Add $2 w$ to both sides of the equation.

$26 w - 2 + 2 w = - 14$

Add $26 w$ and $2 w$ .

$28 w - 2 = - 14$

Step 4

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

Add $2$ to both sides of the equation.

$28 w = - 14 + 2$

Add $- 14$ and $2$ .

$28 w = - 12$

Step 5

Divide each term in $28 w = - 12$ by $28$ and simplify.

Divide each term in $28 w = - 12$ by $28$ .

$\frac{28 w}{28} = \frac{- 12}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 w}{28} = \frac{- 12}{28}$

Divide $w$ by $1$ .

$w = \frac{- 12}{28}$

Simplify the right side.

Cancel the common factor of $- 12$ and $28$ .

Factor $4$ out of $- 12$ .

$w = \frac{4 (- 3)}{28}$

Cancel the common factors.

Factor $4$ out of $28$ .

$w = \frac{4 \cdot - 3}{4 \cdot 7}$

Cancel the common factor.

$w = \frac{4 \cdot - 3}{4 \cdot 7}$

Rewrite the expression.

$w = \frac{- 3}{7}$

Move the negative in front of the fraction.

$w = - \frac{3}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{3}{7}$

Decimal Form:

$w = - 0.\overline{428571}$

Solve for w 30w-(-w+6)+(-5w+4)=-(5w+6)+(-8+3w)

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