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

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

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 4 by x+1.

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

Combine 4x and 6x to get 10x.

$$10x+4-9-\left(2x-3\right)=2\left(1-1\right)$$

Subtract 9 from 4 to get -5.

$$10x-5-\left(2x-3\right)=2\left(1-1\right)$$

To find the opposite of 2x-3, find the opposite of each term.

$$10x-5-2x-\left(-3\right)=2\left(1-1\right)$$

The opposite of -3 is 3.

$$10x-5-2x+3=2\left(1-1\right)$$

Combine 10x and -2x to get 8x.

$$8x-5+3=2\left(1-1\right)$$

Add -5 and 3 to get -2.

$$8x-2=2\left(1-1\right)$$

Subtract 1 from 1 to get 0.

$$8x-2=2\times 0$$

Multiply 2 and 0 to get 0.

$$8x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$8x=2$$

Divide both sides by 8.

$$x=\frac{2}{8}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{4}$$