Solve for x (3x+7)/4-(2x+4)/3=1/12

$\frac{3 x + 7}{4} - \frac{2 x + 4}{3} = \frac{1}{12}$

Step 1

Simplify $\frac{3 x + 7}{4} - \frac{2 x + 4}{3}$ .

Factor $2$ out of $2 x + 4$ .

Factor $2$ out of $2 x$ .

$\frac{3 x + 7}{4} - \frac{2 (x) + 4}{3} = \frac{1}{12}$

Factor $2$ out of $4$ .

$\frac{3 x + 7}{4} - \frac{2 x + 2 \cdot 2}{3} = \frac{1}{12}$

Factor $2$ out of $2 x + 2 \cdot 2$ .

$\frac{3 x + 7}{4} - \frac{2 (x + 2)}{3} = \frac{1}{12}$

To write $\frac{3 x + 7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x + 7}{4} \cdot \frac{3}{3} - \frac{2 (x + 2)}{3} = \frac{1}{12}$

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

$\frac{3 x + 7}{4} \cdot \frac{3}{3} - \frac{2 (x + 2)}{3} \cdot \frac{4}{4} = \frac{1}{12}$

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

Multiply $\frac{3 x + 7}{4}$ by $\frac{3}{3}$ .

$\frac{(3 x + 7) \cdot 3}{4 \cdot 3} - \frac{2 (x + 2)}{3} \cdot \frac{4}{4} = \frac{1}{12}$

Multiply $4$ by $3$ .

$\frac{(3 x + 7) \cdot 3}{12} - \frac{2 (x + 2)}{3} \cdot \frac{4}{4} = \frac{1}{12}$

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

$\frac{(3 x + 7) \cdot 3}{12} - \frac{2 (x + 2) \cdot 4}{3 \cdot 4} = \frac{1}{12}$

Multiply $3$ by $4$ .

$\frac{(3 x + 7) \cdot 3}{12} - \frac{2 (x + 2) \cdot 4}{12} = \frac{1}{12}$

Combine the numerators over the common denominator.

$\frac{(3 x + 7) \cdot 3 - 2 (x + 2) \cdot 4}{12} = \frac{1}{12}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 3 + 7 \cdot 3 - 2 (x + 2) \cdot 4}{12} = \frac{1}{12}$

Multiply $3$ by $3$ .

$\frac{9 x + 7 \cdot 3 - 2 (x + 2) \cdot 4}{12} = \frac{1}{12}$

Multiply $7$ by $3$ .

$\frac{9 x + 21 - 2 (x + 2) \cdot 4}{12} = \frac{1}{12}$

Apply the distributive property.

$\frac{9 x + 21 + (- 2 x - 2 \cdot 2) \cdot 4}{12} = \frac{1}{12}$

Multiply $- 2$ by $2$ .

$\frac{9 x + 21 + (- 2 x - 4) \cdot 4}{12} = \frac{1}{12}$

Apply the distributive property.

$\frac{9 x + 21 - 2 x \cdot 4 - 4 \cdot 4}{12} = \frac{1}{12}$

Multiply $4$ by $- 2$ .

$\frac{9 x + 21 - 8 x - 4 \cdot 4}{12} = \frac{1}{12}$

Multiply $- 4$ by $4$ .

$\frac{9 x + 21 - 8 x - 16}{12} = \frac{1}{12}$

Subtract $8 x$ from $9 x$ .

$\frac{x + 21 - 16}{12} = \frac{1}{12}$

Subtract $16$ from $21$ .

$\frac{x + 5}{12} = \frac{1}{12}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x + 5 = 1$

Step 3

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

Subtract $5$ from both sides of the equation.

$x = 1 - 5$

Subtract $5$ from $1$ .

$x = - 4$

Solve for x (3x+7)/4-(2x+4)/3=1/12

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