Solve for w w/3+4=w/5

$\frac{w}{3} + 4 = \frac{w}{5}$

Step 1

Multiply both sides by $5$ .

$(\frac{w}{3} + 4) \cdot 5 = \frac{w}{5} \cdot 5$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{w}{3} + 4) \cdot 5$ .

Simplify terms.

Apply the distributive property.

$\frac{w}{3} \cdot 5 + 4 \cdot 5 = \frac{w}{5} \cdot 5$

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

$\frac{w \cdot 5}{3} + 4 \cdot 5 = \frac{w}{5} \cdot 5$

Multiply $4$ by $5$ .

$\frac{w \cdot 5}{3} + 20 = \frac{w}{5} \cdot 5$

Move $5$ to the left of $w$ .

$\frac{5 w}{3} + 20 = \frac{w}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{3} + 20 = \frac{w}{5} \cdot 5$

Rewrite the expression.

$\frac{5 w}{3} + 20 = w$

Step 3

Solve for $w$ .

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

Subtract $w$ from both sides of the equation.

$\frac{5 w}{3} + 20 - w = 0$

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

$\frac{5 w}{3} - w \cdot \frac{3}{3} + 20 = 0$

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

$\frac{5 w}{3} + \frac{- w \cdot 3}{3} + 20 = 0$

Combine the numerators over the common denominator.

$\frac{5 w - w \cdot 3}{3} + 20 = 0$

Simplify each term.

Simplify the numerator.

Factor $w$ out of $5 w - w \cdot 3$ .

Factor $w$ out of $5 w$ .

$\frac{w \cdot 5 - w \cdot 3}{3} + 20 = 0$

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

$\frac{w \cdot 5 + w (- 1 \cdot 3)}{3} + 20 = 0$

Factor $w$ out of $w \cdot 5 + w (- 1 \cdot 3)$ .

$\frac{w (5 - 1 \cdot 3)}{3} + 20 = 0$

Multiply $- 1$ by $3$ .

$\frac{w (5 - 3)}{3} + 20 = 0$

Subtract $3$ from $5$ .

$\frac{w \cdot 2}{3} + 20 = 0$

Move $2$ to the left of $w$ .

$\frac{2 w}{3} + 20 = 0$

Subtract $20$ from both sides of the equation.

$\frac{2 w}{3} = - 20$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 w}{3} = \frac{3}{2} \cdot - 20$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 w}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 w}{3} = \frac{3}{2} \cdot - 20$

Rewrite the expression.

$\frac{1}{2} (2 w) = \frac{3}{2} \cdot - 20$

Cancel the common factor of $2$ .

Factor $2$ out of $2 w$ .

$\frac{1}{2} (2 (w)) = \frac{3}{2} \cdot - 20$

Cancel the common factor.

$\frac{1}{2} (2 w) = \frac{3}{2} \cdot - 20$

Rewrite the expression.

$w = \frac{3}{2} \cdot - 20$

Simplify the right side.

Simplify $\frac{3}{2} \cdot - 20$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 20$ .

$w = \frac{3}{2} \cdot (2 (- 10))$

Cancel the common factor.

$w = \frac{3}{2} \cdot (2 \cdot - 10)$

Rewrite the expression.

$w = 3 \cdot - 10$

Multiply $3$ by $- 10$ .

$w = - 30$

Solve for w w/3+4=w/5

Related Questions