Solve for z -7=11/17z

$- 7 = \frac{11}{17} z$

Rewrite the equation as $\frac{11}{17} z = - 7$ .

$\frac{11}{17} z = - 7$

Multiply both sides of the equation by $\frac{17}{11}$ .

$\frac{17}{11} (\frac{11}{17} z) = \frac{17}{11} \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{17}{11} (\frac{11}{17} z)$ .

Combine $\frac{11}{17}$ and $z$ .

$\frac{17}{11} \cdot \frac{11 z}{17} = \frac{17}{11} \cdot - 7$

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17}{11} \cdot \frac{11 z}{17} = \frac{17}{11} \cdot - 7$

Rewrite the expression.

$\frac{1}{11} (11 z) = \frac{17}{11} \cdot - 7$

Cancel the common factor of $11$ .

Factor $11$ out of $11 z$ .

$\frac{1}{11} (11 (z)) = \frac{17}{11} \cdot - 7$

Cancel the common factor.

$\frac{1}{11} (11 z) = \frac{17}{11} \cdot - 7$

Rewrite the expression.

$z = \frac{17}{11} \cdot - 7$

Simplify the right side.

Simplify $\frac{17}{11} \cdot - 7$ .

Multiply $\frac{17}{11} \cdot - 7$ .

Combine $\frac{17}{11}$ and $- 7$ .

$z = \frac{17 \cdot - 7}{11}$

Multiply $17$ by $- 7$ .

$z = \frac{- 119}{11}$

Move the negative in front of the fraction.

$z = - \frac{119}{11}$

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{119}{11}$

Decimal Form:

$z = - 10.\overline{81}$

Mixed Number Form:

$z = - 10 \frac{9}{11}$