Solve for z -1/3(4+z)=-5/6

$- \frac{1}{3} (4 + z) = - \frac{5}{6}$

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{1}{3} \cdot (4 + z)) = - 3 (- \frac{5}{6})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{1}{3} \cdot (4 + z))$ .

Apply the distributive property.

$- 3 (- \frac{1}{3} \cdot 4 - \frac{1}{3} z) = - 3 (- \frac{5}{6})$

Multiply $- \frac{1}{3} \cdot 4$ .

Multiply $4$ by $- 1$ .

$- 3 (- 4 (\frac{1}{3}) - \frac{1}{3} z) = - 3 (- \frac{5}{6})$

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

$- 3 (\frac{- 4}{3} - \frac{1}{3} z) = - 3 (- \frac{5}{6})$

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

$- 3 (\frac{- 4}{3} - \frac{z}{3}) = - 3 (- \frac{5}{6})$

Move the negative in front of the fraction.

$- 3 (- \frac{4}{3} - \frac{z}{3}) = - 3 (- \frac{5}{6})$

Apply the distributive property.

$- 3 (- \frac{4}{3}) - 3 (- \frac{z}{3}) = - 3 (- \frac{5}{6})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$- 3 (\frac{- 4}{3}) - 3 (- \frac{z}{3}) = - 3 (- \frac{5}{6})$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- 4}{3} - 3 (- \frac{z}{3}) = - 3 (- \frac{5}{6})$

Cancel the common factor.

$3 \cdot - 1 \frac{- 4}{3} - 3 (- \frac{z}{3}) = - 3 (- \frac{5}{6})$

Rewrite the expression.

$- - 4 - 3 (- \frac{z}{3}) = - 3 (- \frac{5}{6})$

Multiply $- 1$ by $- 4$ .

$4 - 3 (- \frac{z}{3}) = - 3 (- \frac{5}{6})$

Cancel the common factor of $3$ .

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

$4 - 3 \frac{- z}{3} = - 3 (- \frac{5}{6})$

Factor $3$ out of $- 3$ .

$4 + 3 (- 1) \frac{- z}{3} = - 3 (- \frac{5}{6})$

Cancel the common factor.

$4 + 3 \cdot - 1 \frac{- z}{3} = - 3 (- \frac{5}{6})$

Rewrite the expression.

$4 - - z = - 3 (- \frac{5}{6})$

Multiply.

Multiply $- 1$ by $- 1$ .

$4 + 1 z = - 3 (- \frac{5}{6})$

Multiply $z$ by $1$ .

$4 + z = - 3 (- \frac{5}{6})$

Simplify the right side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$4 + z = - 3 (\frac{- 5}{6})$

Factor $3$ out of $- 3$ .

$4 + z = 3 (- 1) \frac{- 5}{6}$

Factor $3$ out of $6$ .

$4 + z = 3 \cdot - 1 \frac{- 5}{3 \cdot 2}$

Cancel the common factor.

$4 + z = 3 \cdot - 1 \frac{- 5}{3 \cdot 2}$

Rewrite the expression.

$4 + z = - \frac{- 5}{2}$

Move the negative in front of the fraction.

$4 + z = - - \frac{5}{2}$

Multiply $- - \frac{5}{2}$ .

Multiply $- 1$ by $- 1$ .

$4 + z = 1 (\frac{5}{2})$

Multiply $\frac{5}{2}$ by $1$ .

$4 + z = \frac{5}{2}$

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

Subtract $4$ from both sides of the equation.

$z = \frac{5}{2} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z = \frac{5}{2} - 4 \cdot \frac{2}{2}$

Combine $- 4$ and $\frac{2}{2}$ .

$z = \frac{5}{2} + \frac{- 4 \cdot 2}{2}$

Combine the numerators over the common denominator.

$z = \frac{5 - 4 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 4$ by $2$ .

$z = \frac{5 - 8}{2}$

Subtract $8$ from $5$ .

$z = \frac{- 3}{2}$

Move the negative in front of the fraction.

$z = - \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{3}{2}$

Decimal Form:

$z = - 1.5$

Mixed Number Form:

$z = - 1 \frac{1}{2}$

Solve for z -1/3(4+z)=-5/6

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