Solve for z (7z)/3-2=3z-9

$\frac{7 z}{3} - 2 = 3 z - 9$

Move all terms containing $z$ to the left side of the equation.

Subtract $3 z$ from both sides of the equation.

$\frac{7 z}{3} - 2 - 3 z = - 9$

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

$\frac{7 z}{3} - 3 z \cdot \frac{3}{3} - 2 = - 9$

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

$\frac{7 z}{3} + \frac{- 3 z \cdot 3}{3} - 2 = - 9$

Combine the numerators over the common denominator.

$\frac{7 z - 3 z \cdot 3}{3} - 2 = - 9$

Simplify each term.

Simplify the numerator.

Factor $z$ out of $7 z - 3 z \cdot 3$ .

Factor $z$ out of $7 z$ .

$\frac{z \cdot 7 - 3 z \cdot 3}{3} - 2 = - 9$

Factor $z$ out of $- 3 z \cdot 3$ .

$\frac{z \cdot 7 + z (- 3 \cdot 3)}{3} - 2 = - 9$

Factor $z$ out of $z \cdot 7 + z (- 3 \cdot 3)$ .

$\frac{z (7 - 3 \cdot 3)}{3} - 2 = - 9$

Multiply $- 3$ by $3$ .

$\frac{z (7 - 9)}{3} - 2 = - 9$

Subtract $9$ from $7$ .

$\frac{z \cdot - 2}{3} - 2 = - 9$

Move $- 2$ to the left of $z$ .

$\frac{- 2 \cdot z}{3} - 2 = - 9$

Move the negative in front of the fraction.

$- \frac{2 z}{3} - 2 = - 9$

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

Add $2$ to both sides of the equation.

$- \frac{2 z}{3} = - 9 + 2$

Add $- 9$ and $2$ .

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

Multiply both sides of the equation by $- \frac{3}{2}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{2} (- \frac{2 z}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2 z}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 z}{3} = - \frac{3}{2} \cdot - 7$

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{2} (- 2 z) = - \frac{3}{2} \cdot - 7$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 z$ .

$\frac{- 1}{2} (2 (- z)) = - \frac{3}{2} \cdot - 7$

Cancel the common factor.

$\frac{- 1}{2} (2 (- z)) = - \frac{3}{2} \cdot - 7$

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $z$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{3}{2} \cdot - 7$ .

Multiply $- 7$ by $- 1$ .

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

Combine $7$ and $\frac{3}{2}$ .

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

Multiply $7$ by $3$ .

$z = \frac{21}{2}$

The result can be shown in multiple forms.

Exact Form:

$z = \frac{21}{2}$

Decimal Form:

$z = 10.5$

Mixed Number Form:

$z = 10 \frac{1}{2}$

Solve for z (7z)/3-2=3z-9

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