Solve for g 1/4(7+3g)=-g/8

$\frac{1}{4} (7 + 3 g) = - \frac{g}{8}$

Multiply both sides by $8$ .

$\frac{1}{4} \cdot (7 + 3 g) \cdot 8 = - \frac{g}{8} \cdot 8$

Simplify.

Simplify the left side.

Simplify $\frac{1}{4} \cdot (7 + 3 g) \cdot 8$ .

Apply the distributive property.

$(\frac{1}{4} \cdot 7 + \frac{1}{4} (3 g)) \cdot 8 = - \frac{g}{8} \cdot 8$

Combine $\frac{1}{4}$ and $7$ .

$(\frac{7}{4} + \frac{1}{4} (3 g)) \cdot 8 = - \frac{g}{8} \cdot 8$

Multiply $\frac{1}{4} (3 g)$ .

Combine $3$ and $\frac{1}{4}$ .

$(\frac{7}{4} + \frac{3}{4} g) \cdot 8 = - \frac{g}{8} \cdot 8$

Combine $\frac{3}{4}$ and $g$ .

$(\frac{7}{4} + \frac{3 g}{4}) \cdot 8 = - \frac{g}{8} \cdot 8$

Apply the distributive property.

$\frac{7}{4} \cdot 8 + \frac{3 g}{4} \cdot 8 = - \frac{g}{8} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{7}{4} \cdot (4 (2)) + \frac{3 g}{4} \cdot 8 = - \frac{g}{8} \cdot 8$

Cancel the common factor.

$\frac{7}{4} \cdot (4 \cdot 2) + \frac{3 g}{4} \cdot 8 = - \frac{g}{8} \cdot 8$

Rewrite the expression.

$7 \cdot 2 + \frac{3 g}{4} \cdot 8 = - \frac{g}{8} \cdot 8$

Multiply $7$ by $2$ .

$14 + \frac{3 g}{4} \cdot 8 = - \frac{g}{8} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$14 + \frac{3 g}{4} \cdot (4 (2)) = - \frac{g}{8} \cdot 8$

Cancel the common factor.

$14 + \frac{3 g}{4} \cdot (4 \cdot 2) = - \frac{g}{8} \cdot 8$

Rewrite the expression.

$14 + 3 g \cdot 2 = - \frac{g}{8} \cdot 8$

Simplify the expression.

Multiply $2$ by $3$ .

$14 + 6 g = - \frac{g}{8} \cdot 8$

Reorder $14$ and $6 g$ .

$6 g + 14 = - \frac{g}{8} \cdot 8$

Simplify the right side.

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{g}{8}$ into the numerator.

$6 g + 14 = \frac{- g}{8} \cdot 8$

Cancel the common factor.

$6 g + 14 = \frac{- g}{8} \cdot 8$

Rewrite the expression.

$6 g + 14 = - g$

Solve for $g$ .

Move all terms containing $g$ to the left side of the equation.

Add $g$ to both sides of the equation.

$6 g + 14 + g = 0$

Add $6 g$ and $g$ .

$7 g + 14 = 0$

Subtract $14$ from both sides of the equation.

$7 g = - 14$

Divide each term in $7 g = - 14$ by $7$ and simplify.

Divide each term in $7 g = - 14$ by $7$ .

$\frac{7 g}{7} = \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 g}{7} = \frac{- 14}{7}$

Divide $g$ by $1$ .

$g = \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$g = - 2$

Solve for g 1/4(7+3g)=-g/8

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