Solve x+1*x-1/3-1/3x-2^2+2x-1/4=2/3-frac{x+1}{4}-frac{23}{12}

$$\frac{ x+1 \times x-1 }{ 3 } - \frac{ 1 }{ 3 } x- { 2 }^{ 2 } + \frac{ 2x-1 }{ 4 } = \frac{ 2 }{ 3 } - \frac{ x+1 }{ 4 } - \frac{ 23 }{ 12 }$$

Solve for x

$$x = \frac{37}{13} = 2\frac{11}{13} \approx 2.846153846$$

Steps for Solving Linear Equation

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

$$12\left(\frac{x+1x-1}{3}-\frac{1}{3}x-2^{2}\right)+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Combine x and 1x to get 2x.

$$12\left(\frac{2x-1}{3}-\frac{1}{3}x-2^{2}\right)+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Calculate 2 to the power of 2 and get 4.

$$12\left(\frac{2x-1}{3}-\frac{1}{3}x-4\right)+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Use the distributive property to multiply 12 by \frac{2x-1}{3}-\frac{1}{3}x-4.

$$12\times \frac{2x-1}{3}+12\left(-\frac{1}{3}\right)x-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Cancel out 3, the greatest common factor in 12 and 3.

$$4\left(2x-1\right)+12\left(-\frac{1}{3}\right)x-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Use the distributive property to multiply 4 by 2x-1.

$$8x-4+12\left(-\frac{1}{3}\right)x-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Express 12\left(-\frac{1}{3}\right) as a single fraction.

$$8x-4+\frac{12\left(-1\right)}{3}x-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Multiply 12 and -1 to get -12.

$$8x-4+\frac{-12}{3}x-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Divide -12 by 3 to get -4.

$$8x-4-4x-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

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

$$4x-4-48+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Subtract 48 from -4 to get -52.

$$4x-52+3\left(2x-1\right)=8-3\left(x+1\right)-23$$

Use the distributive property to multiply 3 by 2x-1.

$$4x-52+6x-3=8-3\left(x+1\right)-23$$

Combine 4x and 6x to get 10x.

$$10x-52-3=8-3\left(x+1\right)-23$$

Subtract 3 from -52 to get -55.

$$10x-55=8-3\left(x+1\right)-23$$

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

$$10x-55=8-3x-3-23$$

Subtract 3 from 8 to get 5.

$$10x-55=5-3x-23$$

Subtract 23 from 5 to get -18.

$$10x-55=-18-3x$$

Add 3x to both sides.

$$10x-55+3x=-18$$

Combine 10x and 3x to get 13x.

$$13x-55=-18$$

Add 55 to both sides.

$$13x=-18+55$$

Add -18 and 55 to get 37.

$$13x=37$$

Divide both sides by 13.

$$x=\frac{37}{13}$$