Solve 2x-1/6-x-3/9=2+3x/4-3x+4/12

$$\frac { 2 x - 1 } { 6 } - \frac { x - 3 } { 9 } = \frac { 2 + 3 x } { 4 } - \frac { 3 x + 4 } { 12 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 6,9,4,12.

$$6\left(2x-1\right)-4\left(x-3\right)=9\left(2+3x\right)-3\left(3x+4\right)$$

Use the distributive property to multiply 6 by 2x-1.

$$12x-6-4\left(x-3\right)=9\left(2+3x\right)-3\left(3x+4\right)$$

Use the distributive property to multiply -4 by x-3.

$$12x-6-4x+12=9\left(2+3x\right)-3\left(3x+4\right)$$

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

$$8x-6+12=9\left(2+3x\right)-3\left(3x+4\right)$$

Add -6 and 12 to get 6.

$$8x+6=9\left(2+3x\right)-3\left(3x+4\right)$$

Use the distributive property to multiply 9 by 2+3x.

$$8x+6=18+27x-3\left(3x+4\right)$$

Use the distributive property to multiply -3 by 3x+4.

$$8x+6=18+27x-9x-12$$

Combine 27x and -9x to get 18x.

$$8x+6=18+18x-12$$

Subtract 12 from 18 to get 6.

$$8x+6=6+18x$$

Subtract 18x from both sides.

$$8x+6-18x=6$$

Combine 8x and -18x to get -10x.

$$-10x+6=6$$

Subtract 6 from both sides.

$$-10x=6-6$$

Subtract 6 from 6 to get 0.

$$-10x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -10 is not equal to 0, x must be equal to 0.

$$x=0$$