Solve 2x+1/4+2x-1/6=3/22x-1/3-x-1+frac{1}{3}x

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

Solve for x

$$x = -\frac{19}{6} = -3\frac{1}{6} \approx -3.166666667$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Combine 6x and 4x to get 10x.

$$10x+3-2=6\left(2x-1\right)-12x-12+4x$$

Subtract 2 from 3 to get 1.

$$10x+1=6\left(2x-1\right)-12x-12+4x$$

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

$$10x+1=12x-6-12x-12+4x$$

Combine 12x and -12x to get 0.

$$10x+1=-6-12+4x$$

Subtract 12 from -6 to get -18.

$$10x+1=-18+4x$$

Subtract 4x from both sides.

$$10x+1-4x=-18$$

Combine 10x and -4x to get 6x.

$$6x+1=-18$$

Subtract 1 from both sides.

$$6x=-18-1$$

Subtract 1 from -18 to get -19.

$$6x=-19$$

Divide both sides by 6.

$$x=\frac{-19}{6}$$

Fraction \frac{-19}{6} can be rewritten as -\frac{19}{6} by extracting the negative sign.

$$x=-\frac{19}{6}$$