Solve for w (6w-1)/5-3w=(12w-16)/15

$\frac{6 w - 1}{5} - 3 w = \frac{12 w - 16}{15}$

Multiply both sides by $15$ .

$(\frac{6 w - 1}{5} - 3 w) \cdot 15 = \frac{12 w - 16}{15} \cdot 15$

Simplify.

Simplify the left side.

Simplify $(\frac{6 w - 1}{5} - 3 w) \cdot 15$ .

To write $- 3 w$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{6 w - 1}{5} - 3 w \cdot \frac{5}{5}) \cdot 15 = \frac{12 w - 16}{15} \cdot 15$

Simplify terms.

Combine $- 3 w$ and $\frac{5}{5}$ .

$(\frac{6 w - 1}{5} + \frac{- 3 w \cdot 5}{5}) \cdot 15 = \frac{12 w - 16}{15} \cdot 15$

Combine the numerators over the common denominator.

$\frac{6 w - 1 - 3 w \cdot 5}{5} \cdot 15 = \frac{12 w - 16}{15} \cdot 15$

Simplify the numerator.

Multiply $5$ by $- 3$ .

$\frac{6 w - 1 - 15 w}{5} \cdot 15 = \frac{12 w - 16}{15} \cdot 15$

Subtract $15 w$ from $6 w$ .

$\frac{- 9 w - 1}{5} \cdot 15 = \frac{12 w - 16}{15} \cdot 15$

Simplify terms.

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{- 9 w - 1}{5} \cdot (5 (3)) = \frac{12 w - 16}{15} \cdot 15$

Cancel the common factor.

$\frac{- 9 w - 1}{5} \cdot (5 \cdot 3) = \frac{12 w - 16}{15} \cdot 15$

Rewrite the expression.

$(- 9 w - 1) \cdot 3 = \frac{12 w - 16}{15} \cdot 15$

Apply the distributive property.

$- 9 w \cdot 3 - 1 \cdot 3 = \frac{12 w - 16}{15} \cdot 15$

Multiply.

Multiply $3$ by $- 9$ .

$- 27 w - 1 \cdot 3 = \frac{12 w - 16}{15} \cdot 15$

Multiply $- 1$ by $3$ .

$- 27 w - 3 = \frac{12 w - 16}{15} \cdot 15$

Simplify the right side.

Simplify $\frac{12 w - 16}{15} \cdot 15$ .

Factor $4$ out of $12 w - 16$ .

Factor $4$ out of $12 w$ .

$- 27 w - 3 = \frac{4 (3 w) - 16}{15} \cdot 15$

Factor $4$ out of $- 16$ .

$- 27 w - 3 = \frac{4 (3 w) + 4 (- 4)}{15} \cdot 15$

Factor $4$ out of $4 (3 w) + 4 (- 4)$ .

$- 27 w - 3 = \frac{4 (3 w - 4)}{15} \cdot 15$

Cancel the common factor of $15$ .

Cancel the common factor.

$- 27 w - 3 = \frac{4 (3 w - 4)}{15} \cdot 15$

Rewrite the expression.

$- 27 w - 3 = 4 (3 w - 4)$

Apply the distributive property.

$- 27 w - 3 = 4 (3 w) + 4 \cdot - 4$

Multiply.

Multiply $3$ by $4$ .

$- 27 w - 3 = 12 w + 4 \cdot - 4$

Multiply $4$ by $- 4$ .

$- 27 w - 3 = 12 w - 16$

Solve for $w$ .

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

Subtract $12 w$ from both sides of the equation.

$- 27 w - 3 - 12 w = - 16$

Subtract $12 w$ from $- 27 w$ .

$- 39 w - 3 = - 16$

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

Add $3$ to both sides of the equation.

$- 39 w = - 16 + 3$

Add $- 16$ and $3$ .

$- 39 w = - 13$

Divide each term in $- 39 w = - 13$ by $- 39$ and simplify.

Divide each term in $- 39 w = - 13$ by $- 39$ .

$\frac{- 39 w}{- 39} = \frac{- 13}{- 39}$

Simplify the left side.

Cancel the common factor of $- 39$ .

Cancel the common factor.

$\frac{- 39 w}{- 39} = \frac{- 13}{- 39}$

Divide $w$ by $1$ .

$w = \frac{- 13}{- 39}$

Simplify the right side.

Cancel the common factor of $- 13$ and $- 39$ .

Factor $- 13$ out of $- 13$ .

$w = \frac{- 13 (1)}{- 39}$

Cancel the common factors.

Factor $- 13$ out of $- 39$ .

$w = \frac{- 13 \cdot 1}{- 13 \cdot 3}$

Cancel the common factor.

$w = \frac{- 13 \cdot 1}{- 13 \cdot 3}$

Rewrite the expression.

$w = \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$w = \frac{1}{3}$

Decimal Form:

$w = 0.\overline{3}$

Solve for w (6w-1)/5-3w=(12w-16)/15

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