Solve 3x-1/3+1=3x+5/4-x-4/6-21/2

$$\frac { 3 x - 1 } { 3 } + 1 = \frac { 3 x + 5 } { 4 } - \frac { x - 4 } { 6 } - 2 \frac { 1 } { 2 }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6,2.

$$4\left(3x-1\right)+12=3\left(3x+5\right)-2\left(x-4\right)-6\left(2\times 2+1\right)$$

Use the distributive property to multiply 4 by 3x-1.

$$12x-4+12=3\left(3x+5\right)-2\left(x-4\right)-6\left(2\times 2+1\right)$$

Add -4 and 12 to get 8.

$$12x+8=3\left(3x+5\right)-2\left(x-4\right)-6\left(2\times 2+1\right)$$

Use the distributive property to multiply 3 by 3x+5.

$$12x+8=9x+15-2\left(x-4\right)-6\left(2\times 2+1\right)$$

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

$$12x+8=9x+15-2x+8-6\left(2\times 2+1\right)$$

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

$$12x+8=7x+15+8-6\left(2\times 2+1\right)$$

Add 15 and 8 to get 23.

$$12x+8=7x+23-6\left(2\times 2+1\right)$$

Multiply 2 and 2 to get 4.

$$12x+8=7x+23-6\left(4+1\right)$$

Add 4 and 1 to get 5.

$$12x+8=7x+23-6\times 5$$

Multiply -6 and 5 to get -30.

$$12x+8=7x+23-30$$

Subtract 30 from 23 to get -7.

$$12x+8=7x-7$$

Subtract 7x from both sides.

$$12x+8-7x=-7$$

Combine 12x and -7x to get 5x.

$$5x+8=-7$$

Subtract 8 from both sides.

$$5x=-7-8$$

Subtract 8 from -7 to get -15.

$$5x=-15$$

Divide both sides by 5.

$$x=\frac{-15}{5}$$

Divide -15 by 5 to get -3.

$$x=-3$$