Solve for d 5/6d+3=1/2(1-2/3d)

$\frac{5}{6} d + 3 = \frac{1}{2} (1 - \frac{2}{3} d)$

Combine $\frac{5}{6}$ and $d$ .

$\frac{5 d}{6} + 3 = \frac{1}{2} \cdot (1 - \frac{2}{3} d)$

Simplify $\frac{1}{2} \cdot (1 - \frac{2}{3} d)$ .

Simplify each term.

Combine $d$ and $\frac{2}{3}$ .

$\frac{5 d}{6} + 3 = \frac{1}{2} \cdot (1 - \frac{d \cdot 2}{3})$

Move $2$ to the left of $d$ .

$\frac{5 d}{6} + 3 = \frac{1}{2} \cdot (1 - \frac{2 d}{3})$

Simplify terms.

Apply the distributive property.

$\frac{5 d}{6} + 3 = \frac{1}{2} \cdot 1 + \frac{1}{2} (- \frac{2 d}{3})$

Multiply $\frac{1}{2}$ by $1$ .

$\frac{5 d}{6} + 3 = \frac{1}{2} + \frac{1}{2} (- \frac{2 d}{3})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2 d}{3}$ into the numerator.

$\frac{5 d}{6} + 3 = \frac{1}{2} + \frac{1}{2} \cdot \frac{- 2 d}{3}$

Factor $2$ out of $- 2 d$ .

$\frac{5 d}{6} + 3 = \frac{1}{2} + \frac{1}{2} \cdot \frac{2 (- d)}{3}$

Cancel the common factor.

$\frac{5 d}{6} + 3 = \frac{1}{2} + \frac{1}{2} \cdot \frac{2 (- d)}{3}$

Rewrite the expression.

$\frac{5 d}{6} + 3 = \frac{1}{2} + \frac{- d}{3}$

Move the negative in front of the fraction.

$\frac{5 d}{6} + 3 = \frac{1}{2} - \frac{d}{3}$

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

Add $\frac{d}{3}$ to both sides of the equation.

$\frac{5 d}{6} + 3 + \frac{d}{3} = \frac{1}{2}$

To write $\frac{d}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 d}{6} + \frac{d}{3} \cdot \frac{2}{2} + 3 = \frac{1}{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{d}{3}$ by $\frac{2}{2}$ .

$\frac{5 d}{6} + \frac{d \cdot 2}{3 \cdot 2} + 3 = \frac{1}{2}$

Multiply $3$ by $2$ .

$\frac{5 d}{6} + \frac{d \cdot 2}{6} + 3 = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{5 d + d \cdot 2}{6} + 3 = \frac{1}{2}$

Add $5 d$ and $d \cdot 2$ .

Reorder $d$ and $2$ .

$\frac{5 d + 2 \cdot d}{6} + 3 = \frac{1}{2}$

Add $5 d$ and $2 \cdot d$ .

$\frac{7 d}{6} + 3 = \frac{1}{2}$

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

Subtract $3$ from both sides of the equation.

$\frac{7 d}{6} = \frac{1}{2} - 3$

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

$\frac{7 d}{6} = \frac{1}{2} - 3 \cdot \frac{2}{2}$

Combine $- 3$ and $\frac{2}{2}$ .

$\frac{7 d}{6} = \frac{1}{2} + \frac{- 3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{7 d}{6} = \frac{1 - 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$\frac{7 d}{6} = \frac{1 - 6}{2}$

Subtract $6$ from $1$ .

$\frac{7 d}{6} = \frac{- 5}{2}$

Move the negative in front of the fraction.

$\frac{7 d}{6} = - \frac{5}{2}$

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 d}{6} = \frac{6}{7} (- \frac{5}{2})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{7} \cdot \frac{7 d}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 d}{6} = \frac{6}{7} (- \frac{5}{2})$

Rewrite the expression.

$\frac{1}{7} (7 d) = \frac{6}{7} (- \frac{5}{2})$

Cancel the common factor of $7$ .

Factor $7$ out of $7 d$ .

$\frac{1}{7} (7 (d)) = \frac{6}{7} (- \frac{5}{2})$

Cancel the common factor.

$\frac{1}{7} (7 d) = \frac{6}{7} (- \frac{5}{2})$

Rewrite the expression.

$d = \frac{6}{7} (- \frac{5}{2})$

Simplify the right side.

Simplify $\frac{6}{7} (- \frac{5}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$d = \frac{6}{7} \cdot \frac{- 5}{2}$

Factor $2$ out of $6$ .

$d = \frac{2 (3)}{7} \cdot \frac{- 5}{2}$

Cancel the common factor.

$d = \frac{2 \cdot 3}{7} \cdot \frac{- 5}{2}$

Rewrite the expression.

$d = \frac{3}{7} \cdot - 5$

Combine $\frac{3}{7}$ and $- 5$ .

$d = \frac{3 \cdot - 5}{7}$

Simplify the expression.

Multiply $3$ by $- 5$ .

$d = \frac{- 15}{7}$

Move the negative in front of the fraction.

$d = - \frac{15}{7}$

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{15}{7}$

Decimal Form:

$d = - 2.\overline{142857}$

Mixed Number Form:

$d = - 2 \frac{1}{7}$

Solve for d 5/6d+3=1/2(1-2/3d)

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