Solve for d -2 2/3+d/6=2/3

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

Step 1

Simplify the left side.

Convert $2 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $2$ and $\frac{2}{3}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

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

Add $6$ and $2$ .

$- \frac{8}{3} + \frac{d}{6} = \frac{2}{3}$

Step 2

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

Add $\frac{8}{3}$ to both sides of the equation.

$\frac{d}{6} = \frac{2}{3} + \frac{8}{3}$

Combine the numerators over the common denominator.

$\frac{d}{6} = \frac{2 + 8}{3}$

Add $2$ and $8$ .

$\frac{d}{6} = \frac{10}{3}$

Step 3

Multiply both sides of the equation by $6$ .

$6 \frac{d}{6} = 6 (\frac{10}{3})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{d}{6} = 6 (\frac{10}{3})$

Rewrite the expression.

$d = 6 (\frac{10}{3})$

Simplify the right side.

Simplify $6 (\frac{10}{3})$ .

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$d = 3 (2) \frac{10}{3}$

Cancel the common factor.

$d = 3 \cdot 2 \frac{10}{3}$

Rewrite the expression.

$d = 2 \cdot 10$

Multiply $2$ by $10$ .

$d = 20$

Solve for d -2 2/3+d/6=2/3

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