Solve for x (2x-4)/3+(x+7)/12=-9

$\frac{2 x - 4}{3} + \frac{x + 7}{12} = - 9$

Simplify $\frac{2 x - 4}{3} + \frac{x + 7}{12}$ .

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 4$ .

$\frac{2 x + 2 \cdot - 2}{3} + \frac{x + 7}{12} = - 9$

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

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

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

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

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

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

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

Multiply $3$ by $4$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $- 2$ .

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

Apply the distributive property.

$\frac{2 x \cdot 4 - 4 \cdot 4 + x + 7}{12} = - 9$

Multiply $4$ by $2$ .

$\frac{8 x - 4 \cdot 4 + x + 7}{12} = - 9$

Multiply $- 4$ by $4$ .

$\frac{8 x - 16 + x + 7}{12} = - 9$

Add $8 x$ and $x$ .

$\frac{9 x - 16 + 7}{12} = - 9$

Add $- 16$ and $7$ .

$\frac{9 x - 9}{12} = - 9$

Factor $9$ out of $9 x - 9$ .

Factor $9$ out of $9 x$ .

$\frac{9 (x) - 9}{12} = - 9$

Factor $9$ out of $- 9$ .

$\frac{9 (x) + 9 (- 1)}{12} = - 9$

Factor $9$ out of $9 (x) + 9 (- 1)$ .

$\frac{9 (x - 1)}{12} = - 9$

Cancel the common factor of $9$ and $12$ .

Factor $3$ out of $9 (x - 1)$ .

$\frac{3 (3 (x - 1))}{12} = - 9$

Cancel the common factors.

Factor $3$ out of $12$ .

$\frac{3 (3 (x - 1))}{3 (4)} = - 9$

Cancel the common factor.

$\frac{3 (3 (x - 1))}{3 \cdot 4} = - 9$

Rewrite the expression.

$\frac{3 (x - 1)}{4} = - 9$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 (x - 1)}{4} = \frac{4}{3} \cdot - 9$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 (x - 1)}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 (x - 1)}{4} = \frac{4}{3} \cdot - 9$

Rewrite the expression.

$\frac{1}{3} (3 (x - 1)) = \frac{4}{3} \cdot - 9$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{3} (3 (x - 1)) = \frac{4}{3} \cdot - 9$

Rewrite the expression.

$x - 1 = \frac{4}{3} \cdot - 9$

Simplify the right side.

Simplify $\frac{4}{3} \cdot - 9$ .

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

$x - 1 = \frac{4}{3} \cdot (3 (- 3))$

Cancel the common factor.

$x - 1 = \frac{4}{3} \cdot (3 \cdot - 3)$

Rewrite the expression.

$x - 1 = 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$x - 1 = - 12$

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

Add $1$ to both sides of the equation.

$x = - 12 + 1$

Add $- 12$ and $1$ .

$x = - 11$

Solve for x (2x-4)/3+(x+7)/12=-9

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