Solve 2x+a/3x-9z+2/6x=z-a/2x+4a/3x

$$\frac { 2 x + a } { 3 x } - \frac { 9 z + 2 } { 6 x } = \frac { z - a } { 2 x } + \frac { 4 a } { 3 x }$$

Solve for a

$$a=\frac{4x}{3}-4z-\frac{2}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6x, the least common multiple of 3x,6x,2x.

$$2\left(2x+a\right)-\left(9z+2\right)=3\left(z-a\right)+2\times 4a$$

Use the distributive property to multiply 2 by 2x+a.

$$4x+2a-\left(9z+2\right)=3\left(z-a\right)+2\times 4a$$

To find the opposite of 9z+2, find the opposite of each term.

$$4x+2a-9z-2=3\left(z-a\right)+2\times 4a$$

Use the distributive property to multiply 3 by z-a.

$$4x+2a-9z-2=3z-3a+2\times 4a$$

Multiply 2 and 4 to get 8.

$$4x+2a-9z-2=3z-3a+8a$$

Combine -3a and 8a to get 5a.

$$4x+2a-9z-2=3z+5a$$

Subtract 5a from both sides.

$$4x+2a-9z-2-5a=3z$$

Combine 2a and -5a to get -3a.

$$4x-3a-9z-2=3z$$

Subtract 4x from both sides.

$$-3a-9z-2=3z-4x$$

Add 9z to both sides.

$$-3a-2=3z-4x+9z$$

Combine 3z and 9z to get 12z.

$$-3a-2=12z-4x$$

Add 2 to both sides.

$$-3a=12z-4x+2$$

The equation is in standard form.

$$-3a=2+12z-4x$$

Divide both sides by -3.

$$\frac{-3a}{-3}=\frac{2+12z-4x}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$a=\frac{2+12z-4x}{-3}$$

Divide 12z-4x+2 by -3.

$$a=\frac{4x}{3}-4z-\frac{2}{3}$$

Solve for x

$$x=\frac{3a}{4}+3z+\frac{1}{2}$$

$$a\neq -4z-\frac{2}{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6x, the least common multiple of 3x,6x,2x.

$$2\left(2x+a\right)-\left(9z+2\right)=3\left(z-a\right)+2\times 4a$$

Use the distributive property to multiply 2 by 2x+a.

$$4x+2a-\left(9z+2\right)=3\left(z-a\right)+2\times 4a$$

To find the opposite of 9z+2, find the opposite of each term.

$$4x+2a-9z-2=3\left(z-a\right)+2\times 4a$$

Use the distributive property to multiply 3 by z-a.

$$4x+2a-9z-2=3z-3a+2\times 4a$$

Multiply 2 and 4 to get 8.

$$4x+2a-9z-2=3z-3a+8a$$

Combine -3a and 8a to get 5a.

$$4x+2a-9z-2=3z+5a$$

Subtract 2a from both sides.

$$4x-9z-2=3z+5a-2a$$

Combine 5a and -2a to get 3a.

$$4x-9z-2=3z+3a$$

Add 9z to both sides.

$$4x-2=3z+3a+9z$$

Combine 3z and 9z to get 12z.

$$4x-2=12z+3a$$

Add 2 to both sides.

$$4x=12z+3a+2$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{12z+3a+2}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{12z+3a+2}{4}$$

Divide 12z+3a+2 by 4.

$$x=\frac{3a}{4}+3z+\frac{1}{2}$$

Variable x cannot be equal to 0.

$$x=\frac{3a}{4}+3z+\frac{1}{2}\text{, }x\neq 0$$