Solve for z 39=3/11z+18

$39 = \frac{3}{11} z + 18$

Step 1

Rewrite the equation as $\frac{3}{11} z + 18 = 39$ .

$\frac{3}{11} z + 18 = 39$

Step 2

Combine $\frac{3}{11}$ and $z$ .

$\frac{3 z}{11} + 18 = 39$

Step 3

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

Subtract $18$ from both sides of the equation.

$\frac{3 z}{11} = 39 - 18$

Subtract $18$ from $39$ .

$\frac{3 z}{11} = 21$

Step 4

Multiply both sides of the equation by $\frac{11}{3}$ .

$\frac{11}{3} \cdot \frac{3 z}{11} = \frac{11}{3} \cdot 21$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{11}{3} \cdot \frac{3 z}{11}$ .

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11}{3} \cdot \frac{3 z}{11} = \frac{11}{3} \cdot 21$

Rewrite the expression.

$\frac{1}{3} (3 z) = \frac{11}{3} \cdot 21$

Cancel the common factor of $3$ .

Factor $3$ out of $3 z$ .

$\frac{1}{3} (3 (z)) = \frac{11}{3} \cdot 21$

Cancel the common factor.

$\frac{1}{3} (3 z) = \frac{11}{3} \cdot 21$

Rewrite the expression.

$z = \frac{11}{3} \cdot 21$

Simplify the right side.

Simplify $\frac{11}{3} \cdot 21$ .

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$z = \frac{11}{3} \cdot (3 (7))$

Cancel the common factor.

$z = \frac{11}{3} \cdot (3 \cdot 7)$

Rewrite the expression.

$z = 11 \cdot 7$

Multiply $11$ by $7$ .

$z = 77$