Solve for z 1/2=1/2z-5/7

$\frac{1}{2} = \frac{1}{2} z - \frac{5}{7}$

Rewrite the equation as $\frac{1}{2} z - \frac{5}{7} = \frac{1}{2}$ .

$\frac{1}{2} z - \frac{5}{7} = \frac{1}{2}$

Combine $\frac{1}{2}$ and $z$ .

$\frac{z}{2} - \frac{5}{7} = \frac{1}{2}$

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

Add $\frac{5}{7}$ to both sides of the equation.

$\frac{z}{2} = \frac{1}{2} + \frac{5}{7}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{z}{2} = \frac{1}{2} \cdot \frac{7}{7} + \frac{5}{7}$

To write $\frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{z}{2} = \frac{1}{2} \cdot \frac{7}{7} + \frac{5}{7} \cdot \frac{2}{2}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$\frac{z}{2} = \frac{7}{2 \cdot 7} + \frac{5}{7} \cdot \frac{2}{2}$

Multiply $2$ by $7$ .

$\frac{z}{2} = \frac{7}{14} + \frac{5}{7} \cdot \frac{2}{2}$

Multiply $\frac{5}{7}$ by $\frac{2}{2}$ .

$\frac{z}{2} = \frac{7}{14} + \frac{5 \cdot 2}{7 \cdot 2}$

Multiply $7$ by $2$ .

$\frac{z}{2} = \frac{7}{14} + \frac{5 \cdot 2}{14}$

Combine the numerators over the common denominator.

$\frac{z}{2} = \frac{7 + 5 \cdot 2}{14}$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{z}{2} = \frac{7 + 10}{14}$

Add $7$ and $10$ .

$\frac{z}{2} = \frac{17}{14}$

Multiply both sides of the equation by $2$ .

$2 \frac{z}{2} = 2 (\frac{17}{14})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{z}{2} = 2 (\frac{17}{14})$

Rewrite the expression.

$z = 2 (\frac{17}{14})$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$z = 2 \frac{17}{2 (7)}$

Cancel the common factor.

$z = 2 \frac{17}{2 \cdot 7}$

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$z = 2.\overline{428571}$

Mixed Number Form:

$z = 2 \frac{3}{7}$

Solve for z 1/2=1/2z-5/7

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