Solve for z -2/3+3/7z=1/2

$- \frac{2}{3} + \frac{3}{7} z = \frac{1}{2}$

Combine $\frac{3}{7}$ and $z$ .

$- \frac{2}{3} + \frac{3 z}{7} = \frac{1}{2}$

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

Add $\frac{2}{3}$ to both sides of the equation.

$\frac{3 z}{7} = \frac{1}{2} + \frac{2}{3}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 z}{7} = \frac{1}{2} \cdot \frac{3}{3} + \frac{2}{3}$

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

$\frac{3 z}{7} = \frac{1}{2} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{2}{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

$\frac{3 z}{7} = \frac{3}{6} + \frac{2}{3} \cdot \frac{2}{2}$

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$\frac{3 z}{7} = \frac{3}{6} + \frac{2 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$\frac{3 z}{7} = \frac{3}{6} + \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$\frac{3 z}{7} = \frac{3 + 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{3 z}{7} = \frac{3 + 4}{6}$

Add $3$ and $4$ .

$\frac{3 z}{7} = \frac{7}{6}$

Multiply both sides of the equation by $\frac{7}{3}$ .

$\frac{7}{3} \cdot \frac{3 z}{7} = \frac{7}{3} \cdot \frac{7}{6}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{7}{3} \cdot \frac{3 z}{7}$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7}{3} \cdot \frac{3 z}{7} = \frac{7}{3} \cdot \frac{7}{6}$

Rewrite the expression.

$\frac{1}{3} (3 z) = \frac{7}{3} \cdot \frac{7}{6}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 z$ .

$\frac{1}{3} (3 (z)) = \frac{7}{3} \cdot \frac{7}{6}$

Cancel the common factor.

$\frac{1}{3} (3 z) = \frac{7}{3} \cdot \frac{7}{6}$

Rewrite the expression.

$z = \frac{7}{3} \cdot \frac{7}{6}$

Simplify the right side.

Multiply $\frac{7}{3} \cdot \frac{7}{6}$ .

Multiply $\frac{7}{3}$ by $\frac{7}{6}$ .

$z = \frac{7 \cdot 7}{3 \cdot 6}$

Multiply $7$ by $7$ .

$z = \frac{49}{3 \cdot 6}$

Multiply $3$ by $6$ .

$z = \frac{49}{18}$

The result can be shown in multiple forms.

Exact Form:

$z = \frac{49}{18}$

Decimal Form:

$z = 2.7\overline{2}$

Mixed Number Form:

$z = 2 \frac{13}{18}$

Solve for z -2/3+3/7z=1/2

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