Solve x+6(frac{z_{2}+62}{11})-52=33

$$x + 6 ( \frac { z _ { 2 } + 62 } { 11 } ) - 52 = 33$$

Solve for x

$$x=\frac{563-6z_{2}}{11}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 11.

$$11x+6\left(z_{2}+62\right)-572=363$$

Use the distributive property to multiply 6 by z_{2}+62.

$$11x+6z_{2}+372-572=363$$

Subtract 572 from 372 to get -200.

$$11x+6z_{2}-200=363$$

Subtract 6z_{2} from both sides.

$$11x-200=363-6z_{2}$$

Add 200 to both sides.

$$11x=363-6z_{2}+200$$

Add 363 and 200 to get 563.

$$11x=563-6z_{2}$$

Divide both sides by 11.

$$\frac{11x}{11}=\frac{563-6z_{2}}{11}$$

Dividing by 11 undoes the multiplication by 11.

$$x=\frac{563-6z_{2}}{11}$$

Solve for z_2

$$z_{2}=\frac{563-11x}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 11.

$$11x+6\left(z_{2}+62\right)-572=363$$

Use the distributive property to multiply 6 by z_{2}+62.

$$11x+6z_{2}+372-572=363$$

Subtract 572 from 372 to get -200.

$$11x+6z_{2}-200=363$$

Subtract 11x from both sides.

$$6z_{2}-200=363-11x$$

Add 200 to both sides.

$$6z_{2}=363-11x+200$$

Add 363 and 200 to get 563.

$$6z_{2}=563-11x$$

Divide both sides by 6.

$$\frac{6z_{2}}{6}=\frac{563-11x}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$z_{2}=\frac{563-11x}{6}$$