Solve 2x+a/3x-97+a/6x=2-a/2x+9a/3x

$$\frac { 2 x + a } { 3 x } - \frac { 97 + a } { 6 x } = \frac { 2 - a } { 2 x } + \frac { 9 a } { 3 x }$$

Solve for a

$$a=\frac{2x}{7}-\frac{103}{14}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$2\left(2x+a\right)-\left(97+a\right)=3\left(2-a\right)+2\times 9a$$

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

$$4x+2a-\left(97+a\right)=3\left(2-a\right)+2\times 9a$$

To find the opposite of 97+a, find the opposite of each term.

$$4x+2a-97-a=3\left(2-a\right)+2\times 9a$$

Combine 2a and -a to get a.

$$4x+a-97=3\left(2-a\right)+2\times 9a$$

Use the distributive property to multiply 3 by 2-a.

$$4x+a-97=6-3a+2\times 9a$$

Multiply 2 and 9 to get 18.

$$4x+a-97=6-3a+18a$$

Combine -3a and 18a to get 15a.

$$4x+a-97=6+15a$$

Subtract 15a from both sides.

$$4x+a-97-15a=6$$

Combine a and -15a to get -14a.

$$4x-14a-97=6$$

Subtract 4x from both sides.

$$-14a-97=6-4x$$

Add 97 to both sides.

$$-14a=6-4x+97$$

Add 6 and 97 to get 103.

$$-14a=103-4x$$

Divide both sides by -14.

$$\frac{-14a}{-14}=\frac{103-4x}{-14}$$

Dividing by -14 undoes the multiplication by -14.

$$a=\frac{103-4x}{-14}$$

Divide 103-4x by -14.

$$a=\frac{2x}{7}-\frac{103}{14}$$

Solve for x

$$x=\frac{7a}{2}+\frac{103}{4}$$

$$a\neq -\frac{103}{14}$$

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.

$$2\left(2x+a\right)-\left(97+a\right)=3\left(2-a\right)+2\times 9a$$

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

$$4x+2a-\left(97+a\right)=3\left(2-a\right)+2\times 9a$$

To find the opposite of 97+a, find the opposite of each term.

$$4x+2a-97-a=3\left(2-a\right)+2\times 9a$$

Combine 2a and -a to get a.

$$4x+a-97=3\left(2-a\right)+2\times 9a$$

Use the distributive property to multiply 3 by 2-a.

$$4x+a-97=6-3a+2\times 9a$$

Multiply 2 and 9 to get 18.

$$4x+a-97=6-3a+18a$$

Combine -3a and 18a to get 15a.

$$4x+a-97=6+15a$$

Subtract a from both sides.

$$4x-97=6+15a-a$$

Combine 15a and -a to get 14a.

$$4x-97=6+14a$$

Add 97 to both sides.

$$4x=6+14a+97$$

Add 6 and 97 to get 103.

$$4x=103+14a$$

The equation is in standard form.

$$4x=14a+103$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{14a+103}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{14a+103}{4}$$

Divide 103+14a by 4.

$$x=\frac{7a}{2}+\frac{103}{4}$$

Variable x cannot be equal to 0.

$$x=\frac{7a}{2}+\frac{103}{4}\text{, }x\neq 0$$