Solve for z z-2=4+9z

$z - 2 = 4 + 9 z$

Step 1

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

Subtract $9 z$ from both sides of the equation.

$z - 2 - 9 z = 4$

Subtract $9 z$ from $z$ .

$- 8 z - 2 = 4$

Step 2

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

Add $2$ to both sides of the equation.

$- 8 z = 4 + 2$

Add $4$ and $2$ .

$- 8 z = 6$

Step 3

Divide each term in $- 8 z = 6$ by $- 8$ and simplify.

Divide each term in $- 8 z = 6$ by $- 8$ .

$\frac{- 8 z}{- 8} = \frac{6}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 z}{- 8} = \frac{6}{- 8}$

Divide $z$ by $1$ .

$z = \frac{6}{- 8}$

Simplify the right side.

Cancel the common factor of $6$ and $- 8$ .

Factor $2$ out of $6$ .

$z = \frac{2 (3)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$z = \frac{3}{- 4}$

Move the negative in front of the fraction.

$z = - \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{3}{4}$

Decimal Form:

$z = - 0.75$