Solve for w 4+3/4w=2+2/3w

$4 + \frac{3}{4} w = 2 + \frac{2}{3} w$

Combine $\frac{3}{4}$ and $w$ .

$4 + \frac{3 w}{4} = 2 + \frac{2}{3} w$

Combine $\frac{2}{3}$ and $w$ .

$4 + \frac{3 w}{4} = 2 + \frac{2 w}{3}$

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

Subtract $\frac{2 w}{3}$ from both sides of the equation.

$4 + \frac{3 w}{4} - \frac{2 w}{3} = 2$

To write $\frac{3 w}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 + \frac{3 w}{4} \cdot \frac{3}{3} - \frac{2 w}{3} = 2$

To write $- \frac{2 w}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 + \frac{3 w}{4} \cdot \frac{3}{3} - \frac{2 w}{3} \cdot \frac{4}{4} = 2$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 w}{4}$ by $\frac{3}{3}$ .

$4 + \frac{3 w \cdot 3}{4 \cdot 3} - \frac{2 w}{3} \cdot \frac{4}{4} = 2$

Multiply $4$ by $3$ .

$4 + \frac{3 w \cdot 3}{12} - \frac{2 w}{3} \cdot \frac{4}{4} = 2$

Multiply $\frac{2 w}{3}$ by $\frac{4}{4}$ .

$4 + \frac{3 w \cdot 3}{12} - \frac{2 w \cdot 4}{3 \cdot 4} = 2$

Multiply $3$ by $4$ .

$4 + \frac{3 w \cdot 3}{12} - \frac{2 w \cdot 4}{12} = 2$

Combine the numerators over the common denominator.

$4 + \frac{3 w \cdot 3 - 2 w \cdot 4}{12} = 2$

Simplify each term.

Simplify the numerator.

Factor $w$ out of $3 w \cdot 3 - 2 w \cdot 4$ .

Factor $w$ out of $3 w \cdot 3$ .

$4 + \frac{w (3 \cdot 3) - 2 w \cdot 4}{12} = 2$

Factor $w$ out of $- 2 w \cdot 4$ .

$4 + \frac{w (3 \cdot 3) + w (- 2 \cdot 4)}{12} = 2$

Factor $w$ out of $w (3 \cdot 3) + w (- 2 \cdot 4)$ .

$4 + \frac{w (3 \cdot 3 - 2 \cdot 4)}{12} = 2$

Multiply $3$ by $3$ .

$4 + \frac{w (9 - 2 \cdot 4)}{12} = 2$

Multiply $- 2$ by $4$ .

$4 + \frac{w (9 - 8)}{12} = 2$

Subtract $8$ from $9$ .

$4 + \frac{w \cdot 1}{12} = 2$

Multiply $w$ by $1$ .

$4 + \frac{w}{12} = 2$

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

Subtract $4$ from both sides of the equation.

$\frac{w}{12} = 2 - 4$

Subtract $4$ from $2$ .

$\frac{w}{12} = - 2$

Multiply both sides of the equation by $12$ .

$12 \frac{w}{12} = 12 \cdot - 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{w}{12} = 12 \cdot - 2$

Rewrite the expression.

$w = 12 \cdot - 2$

Simplify the right side.

Multiply $12$ by $- 2$ .

$w = - 24$

Solve for w 4+3/4w=2+2/3w

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