Algebra Examples

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

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

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Step 2.1

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

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Step 2.1.1

Factor $2$ out of $4 w$ .

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

Step 2.1.2

Factor $2$ out of $6$ .

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

Step 2.1.3

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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Step 2.4.1

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

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

Step 2.4.2

Multiply $2$ by $2$ .

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

Step 2.4.3

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

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Simplify the numerator.

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Step 2.6.1

Apply the distributive property.

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

Step 2.6.2

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

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

Step 2.6.3

Multiply $14$ by $2$ .

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

Step 2.6.4

Apply the distributive property.

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

Step 2.6.5

Multiply $2$ by $- 3$ .

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

Step 2.6.6

Multiply $- 3$ by $3$ .

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

Step 2.6.7

Subtract $6 w$ from $2 w$ .

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

Step 2.6.8

Subtract $9$ from $28$ .

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

Step 2.7

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

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

Step 2.8

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

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

Step 2.9

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

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

Step 2.10

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

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

Step 2.11

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 $w$ .

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Step 4.1

Add $19$ to both sides of the equation.

$4 w = 19$

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $w$ by $1$ .

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