Solve for d 4+3/7d=1/7d-8

$4 + \frac{3}{7} d = \frac{1}{7} d - 8$

Step 1

Combine $\frac{3}{7}$ and $d$ .

$4 + \frac{3 d}{7} = \frac{1}{7} d - 8$

Step 2

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

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

Step 3

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

Subtract $\frac{d}{7}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $d$ from $3 d$ .

$4 + \frac{2 d}{7} = - 8$

Step 4

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

Subtract $4$ from both sides of the equation.

$\frac{2 d}{7} = - 8 - 4$

Subtract $4$ from $- 8$ .

$\frac{2 d}{7} = - 12$

Step 5

Multiply both sides of the equation by $\frac{7}{2}$ .

$\frac{7}{2} \cdot \frac{2 d}{7} = \frac{7}{2} \cdot - 12$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{7}{2} \cdot \frac{2 d}{7}$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7}{2} \cdot \frac{2 d}{7} = \frac{7}{2} \cdot - 12$

Rewrite the expression.

$\frac{1}{2} (2 d) = \frac{7}{2} \cdot - 12$

Cancel the common factor of $2$ .

Factor $2$ out of $2 d$ .

$\frac{1}{2} (2 (d)) = \frac{7}{2} \cdot - 12$

Cancel the common factor.

$\frac{1}{2} (2 d) = \frac{7}{2} \cdot - 12$

Rewrite the expression.

$d = \frac{7}{2} \cdot - 12$

Simplify the right side.

Simplify $\frac{7}{2} \cdot - 12$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 12$ .

$d = \frac{7}{2} \cdot (2 (- 6))$

Cancel the common factor.

$d = \frac{7}{2} \cdot (2 \cdot - 6)$

Rewrite the expression.

$d = 7 \cdot - 6$

Multiply $7$ by $- 6$ .

$d = - 42$

Solve for d 4+3/7d=1/7d-8

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