Solve 2x-1/2+2x+3/3=x+1/6-x-1/12+frac{3}{4}x

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

Solve for x

$$x=-\frac{3}{10}=-0.3$$

Steps for Solving Linear Equation

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

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

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

$$12x-6+4\left(2x+3\right)=2\left(x+1\right)-\left(x-1\right)+9x$$

Use the distributive property to multiply 4 by 2x+3.

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

Combine 12x and 8x to get 20x.

$$20x-6+12=2\left(x+1\right)-\left(x-1\right)+9x$$

Add -6 and 12 to get 6.

$$20x+6=2\left(x+1\right)-\left(x-1\right)+9x$$

Use the distributive property to multiply 2 by x+1.

$$20x+6=2x+2-\left(x-1\right)+9x$$

To find the opposite of x-1, find the opposite of each term.

$$20x+6=2x+2-x-\left(-1\right)+9x$$

The opposite of -1 is 1.

$$20x+6=2x+2-x+1+9x$$

Combine 2x and -x to get x.

$$20x+6=x+2+1+9x$$

Add 2 and 1 to get 3.

$$20x+6=x+3+9x$$

Combine x and 9x to get 10x.

$$20x+6=10x+3$$

Subtract 10x from both sides.

$$20x+6-10x=3$$

Combine 20x and -10x to get 10x.

$$10x+6=3$$

Subtract 6 from both sides.

$$10x=3-6$$

Subtract 6 from 3 to get -3.

$$10x=-3$$

Divide both sides by 10.

$$x=\frac{-3}{10}$$

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$x=-\frac{3}{10}$$