Solve for d 7/6d+4/3=-1/3

$\frac{7}{6} d + \frac{4}{3} = - \frac{1}{3}$

Step 1

Combine $\frac{7}{6}$ and $d$ .

$\frac{7 d}{6} + \frac{4}{3} = - \frac{1}{3}$

Step 2

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

Subtract $\frac{4}{3}$ from both sides of the equation.

$\frac{7 d}{6} = - \frac{1}{3} - \frac{4}{3}$

Combine the numerators over the common denominator.

$\frac{7 d}{6} = \frac{- 1 - 4}{3}$

Subtract $4$ from $- 1$ .

$\frac{7 d}{6} = \frac{- 5}{3}$

Move the negative in front of the fraction.

$\frac{7 d}{6} = - \frac{5}{3}$

Step 3

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

$\frac{6}{7} \cdot \frac{7 d}{6} = \frac{6}{7} (- \frac{5}{3})$

Step 4

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.

$\frac{6}{7} \cdot \frac{7 d}{6} = \frac{6}{7} (- \frac{5}{3})$

Rewrite the expression.

$\frac{1}{7} (7 d) = \frac{6}{7} (- \frac{5}{3})$

Cancel the common factor of $7$ .

Factor $7$ out of $7 d$ .

$\frac{1}{7} (7 (d)) = \frac{6}{7} (- \frac{5}{3})$

Cancel the common factor.

$\frac{1}{7} (7 d) = \frac{6}{7} (- \frac{5}{3})$

Rewrite the expression.

$d = \frac{6}{7} (- \frac{5}{3})$

Simplify the right side.

Simplify $\frac{6}{7} (- \frac{5}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$d = \frac{6}{7} \cdot \frac{- 5}{3}$

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{2}{7}$ and $- 5$ .

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

Simplify the expression.

Multiply $2$ by $- 5$ .

$d = \frac{- 10}{7}$

Move the negative in front of the fraction.

$d = - \frac{10}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{10}{7}$

Decimal Form:

$d = - 1.\overline{428571}$

Mixed Number Form:

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

Solve for d 7/6d+4/3=-1/3

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