Solve by Factoring 3/(2g+8)=3/4

$\frac{3}{2 g + 8} = \frac{3}{4}$

Step 1

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

$\frac{3}{2 g + 8} - \frac{3}{4} = 0$

Step 2

Factor $2$ out of $2 g + 8$ .

Factor $2$ out of $2 g$ .

$\frac{3}{2 (g) + 8} - \frac{3}{4} = 0$

Factor $2$ out of $8$ .

$\frac{3}{2 g + 2 \cdot 4} - \frac{3}{4} = 0$

Factor $2$ out of $2 g + 2 \cdot 4$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

Multiply $\frac{3}{2 (g + 4)}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Multiply $\frac{3}{4}$ by $\frac{g + 4}{g + 4}$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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

Factor $3$ out of $3 \cdot 2$ .

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

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

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

Factor $3$ out of $3 (2) + 3 (- (g + 4))$ .

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

Apply the distributive property.

$\frac{3 (2 - g - 1 \cdot 4)}{4 (g + 4)} = 0$

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $2$ .

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

Step 8

Set the numerator equal to zero.

$3 (- g - 2) = 0$

Step 9

Solve the equation for $g$ .

Divide each term in $3 (- g - 2) = 0$ by $3$ and simplify.

Divide each term in $3 (- g - 2) = 0$ by $3$ .

$\frac{3 (- g - 2)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (- g - 2)}{3} = \frac{0}{3}$

Divide $- g - 2$ by $1$ .

$- g - 2 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$- g - 2 = 0$

Add $2$ to both sides of the equation.

$- g = 2$

Divide each term in $- g = 2$ by $- 1$ and simplify.

Divide each term in $- g = 2$ by $- 1$ .

$\frac{- g}{- 1} = \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{g}{1} = \frac{2}{- 1}$

Divide $g$ by $1$ .

$g = \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$g = - 2$

Solve by Factoring 3/(2g+8)=3/4

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