Solve 11/z=3/2-2/5

$$\frac { 11 } { z } = \frac { 3 } { 2 } - \frac { 2 } { 5 }$$

Solve for z

$$z=10$$

Steps for Solving Linear Equation

Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10z, the least common multiple of z,2,5.

$$10\times 11=10z\times \frac{3}{2}+10z\left(-\frac{2}{5}\right)$$

Multiply 10 and 11 to get 110.

$$110=10z\times \frac{3}{2}+10z\left(-\frac{2}{5}\right)$$

Express 10\times \frac{3}{2} as a single fraction.

$$110=\frac{10\times 3}{2}z+10z\left(-\frac{2}{5}\right)$$

Multiply 10 and 3 to get 30.

$$110=\frac{30}{2}z+10z\left(-\frac{2}{5}\right)$$

Divide 30 by 2 to get 15.

$$110=15z+10z\left(-\frac{2}{5}\right)$$

Express 10\left(-\frac{2}{5}\right) as a single fraction.

$$110=15z+\frac{10\left(-2\right)}{5}z$$

Multiply 10 and -2 to get -20.

$$110=15z+\frac{-20}{5}z$$

Divide -20 by 5 to get -4.

$$110=15z-4z$$

Combine 15z and -4z to get 11z.

$$110=11z$$

Swap sides so that all variable terms are on the left hand side.

$$11z=110$$

Divide both sides by 11.

$$z=\frac{110}{11}$$

Divide 110 by 11 to get 10.

$$z=10$$