Solve by Factoring (w+14)/(4w+6)=3/4

$\frac{w + 14}{4 w + 6} = \frac{3}{4}$

Step 1

Subtract $\frac{3}{4}$ from both sides of the equation.

$\frac{w + 14}{4 w + 6} - \frac{3}{4} = 0$

Step 2

Simplify $\frac{w + 14}{4 w + 6} - \frac{3}{4}$ .

Factor $2$ out of $4 w + 6$ .

Factor $2$ out of $4 w$ .

$\frac{w + 14}{2 (2 w) + 6} - \frac{3}{4} = 0$

Factor $2$ out of $6$ .

$\frac{w + 14}{2 (2 w) + 2 (3)} - \frac{3}{4} = 0$

Factor $2$ out of $2 (2 w) + 2 (3)$ .

$\frac{w + 14}{2 (2 w + 3)} - \frac{3}{4} = 0$

To write $\frac{w + 14}{2 (2 w + 3)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{w + 14}{2 (2 w + 3)} \cdot \frac{2}{2} - \frac{3}{4} = 0$

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

$\frac{w + 14}{2 (2 w + 3)} \cdot \frac{2}{2} - \frac{3}{4} \cdot \frac{2 w + 3}{2 w + 3} = 0$

Write each expression with a common denominator of $4 (2 w + 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{w + 14}{2 (2 w + 3)}$ by $\frac{2}{2}$ .

$\frac{(w + 14) \cdot 2}{2 (2 w + 3) \cdot 2} - \frac{3}{4} \cdot \frac{2 w + 3}{2 w + 3} = 0$

Multiply $2$ by $2$ .

$\frac{(w + 14) \cdot 2}{4 (2 w + 3)} - \frac{3}{4} \cdot \frac{2 w + 3}{2 w + 3} = 0$

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

$\frac{(w + 14) \cdot 2}{4 (2 w + 3)} - \frac{3 (2 w + 3)}{4 (2 w + 3)} = 0$

Combine the numerators over the common denominator.

$\frac{(w + 14) \cdot 2 - 3 (2 w + 3)}{4 (2 w + 3)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{w \cdot 2 + 14 \cdot 2 - 3 (2 w + 3)}{4 (2 w + 3)} = 0$

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

$\frac{2 \cdot w + 14 \cdot 2 - 3 (2 w + 3)}{4 (2 w + 3)} = 0$

Multiply $14$ by $2$ .

$\frac{2 \cdot w + 28 - 3 (2 w + 3)}{4 (2 w + 3)} = 0$

Apply the distributive property.

$\frac{2 w + 28 - 3 (2 w) - 3 \cdot 3}{4 (2 w + 3)} = 0$

Multiply $2$ by $- 3$ .

$\frac{2 w + 28 - 6 w - 3 \cdot 3}{4 (2 w + 3)} = 0$

Multiply $- 3$ by $3$ .

$\frac{2 w + 28 - 6 w - 9}{4 (2 w + 3)} = 0$

Subtract $6 w$ from $2 w$ .

$\frac{- 4 w + 28 - 9}{4 (2 w + 3)} = 0$

Subtract $9$ from $28$ .

$\frac{- 4 w + 19}{4 (2 w + 3)} = 0$

Factor $- 1$ out of $- 4 w$ .

$\frac{- (4 w) + 19}{4 (2 w + 3)} = 0$

Rewrite $19$ as $- 1 (- 19)$ .

$\frac{- (4 w) - 1 (- 19)}{4 (2 w + 3)} = 0$

Factor $- 1$ out of $- (4 w) - 1 (- 19)$ .

$\frac{- (4 w - 19)}{4 (2 w + 3)} = 0$

Rewrite $- (4 w - 19)$ as $- 1 (4 w - 19)$ .

$\frac{- 1 (4 w - 19)}{4 (2 w + 3)} = 0$

Move the negative in front of the fraction.

$- \frac{4 w - 19}{4 (2 w + 3)} = 0$

Step 3

Set the numerator equal to zero.

$4 w - 19 = 0$

Step 4

Solve the equation for $w$ .

Add $19$ to both sides of the equation.

$4 w = 19$

Divide each term in $4 w = 19$ by $4$ and simplify.

Divide each term in $4 w = 19$ by $4$ .

$\frac{4 w}{4} = \frac{19}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 w}{4} = \frac{19}{4}$

Divide $w$ by $1$ .

$w = \frac{19}{4}$

Solve by Factoring (w+14)/(4w+6)=3/4

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