Solve 2+x/9-2x-3/6=3-x-7/18-2-3x/12

$$\frac { 2 + x } { 9 } - \frac { 2 x - 3 } { 6 } = 3 - \frac { x - 7 } { 18 } - \frac { 2 - 3 x } { 12 }$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,6,18,12.

$$4\left(2+x\right)-6\left(2x-3\right)=108-2\left(x-7\right)-3\left(2-3x\right)$$

Use the distributive property to multiply 4 by 2+x.

$$8+4x-6\left(2x-3\right)=108-2\left(x-7\right)-3\left(2-3x\right)$$

Use the distributive property to multiply -6 by 2x-3.

$$8+4x-12x+18=108-2\left(x-7\right)-3\left(2-3x\right)$$

Combine 4x and -12x to get -8x.

$$8-8x+18=108-2\left(x-7\right)-3\left(2-3x\right)$$

Add 8 and 18 to get 26.

$$26-8x=108-2\left(x-7\right)-3\left(2-3x\right)$$

Use the distributive property to multiply -2 by x-7.

$$26-8x=108-2x+14-3\left(2-3x\right)$$

Add 108 and 14 to get 122.

$$26-8x=122-2x-3\left(2-3x\right)$$

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

$$26-8x=122-2x-6+9x$$

Subtract 6 from 122 to get 116.

$$26-8x=116-2x+9x$$

Combine -2x and 9x to get 7x.

$$26-8x=116+7x$$

Subtract 7x from both sides.

$$26-8x-7x=116$$

Combine -8x and -7x to get -15x.

$$26-15x=116$$

Subtract 26 from both sides.

$$-15x=116-26$$

Subtract 26 from 116 to get 90.

$$-15x=90$$

Divide both sides by -15.

$$x=\frac{90}{-15}$$

Divide 90 by -15 to get -6.

$$x=-6$$