Solve for z 3z+9+14z=4z+5

$3 z + 9 + 14 z = 4 z + 5$

Step 1

Add $3 z$ and $14 z$ .

$17 z + 9 = 4 z + 5$

Step 2

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

Subtract $4 z$ from both sides of the equation.

$17 z + 9 - 4 z = 5$

Subtract $4 z$ from $17 z$ .

$13 z + 9 = 5$

Step 3

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

Subtract $9$ from both sides of the equation.

$13 z = 5 - 9$

Subtract $9$ from $5$ .

$13 z = - 4$

Step 4

Divide each term in $13 z = - 4$ by $13$ and simplify.

Divide each term in $13 z = - 4$ by $13$ .

$\frac{13 z}{13} = \frac{- 4}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 z}{13} = \frac{- 4}{13}$

Divide $z$ by $1$ .

$z = \frac{- 4}{13}$

Simplify the right side.

Move the negative in front of the fraction.

$z = - \frac{4}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{4}{13}$

Decimal Form:

$z = - 0.\overline{307692}$