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

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

Simplify $\frac{1}{4} + \frac{2 x + 7}{12}$ .

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

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

Multiply $4$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Add $3$ and $7$ .

$\frac{2 x + 10}{12} = - 2$

Factor $2$ out of $2 x + 10$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 10}{12} = - 2$

Factor $2$ out of $10$ .

$\frac{2 x + 2 \cdot 5}{12} = - 2$

Factor $2$ out of $2 x + 2 \cdot 5$ .

$\frac{2 (x + 5)}{12} = - 2$

Cancel the common factors.

Factor $2$ out of $12$ .

$\frac{2 (x + 5)}{2 \cdot 6} = - 2$

Cancel the common factor.

$\frac{2 (x + 5)}{2 \cdot 6} = - 2$

Rewrite the expression.

$\frac{x + 5}{6} = - 2$

Multiply both sides of the equation by $6$ .

$6 \frac{x + 5}{6} = 6 \cdot - 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{x + 5}{6} = 6 \cdot - 2$

Rewrite the expression.

$x + 5 = 6 \cdot - 2$

Simplify the right side.

Multiply $6$ by $- 2$ .

$x + 5 = - 12$

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

Subtract $5$ from both sides of the equation.

$x = - 12 - 5$

Subtract $5$ from $- 12$ .

$x = - 17$