Solve 8x+1/4+(2x-1)/6=3/2(2x-7/3)-[x-(1+frac{1}{3}x)]

$$\frac { 8 x + 1 } { 4 } + \frac { ( 2 x - 1 ) } { 6 } = \frac { 3 } { 2 } ( \frac { 2 x - 7 } { 3 } ) - [ x - ( 1 + \frac { 1 } { 3 } x ) ]$$

Solve for x

$$x = -\frac{31}{24} = -1\frac{7}{24} \approx -1.291666667$$

Steps for Solving Linear Equation

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

$$3\left(8x+1\right)+2\left(2x-1\right)=6\left(2x-7\right)-12\left(x-\left(1+\frac{1}{3}x\right)\right)$$

Use the distributive property to multiply 3 by 8x+1.

$$24x+3+2\left(2x-1\right)=6\left(2x-7\right)-12\left(x-\left(1+\frac{1}{3}x\right)\right)$$

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

$$24x+3+4x-2=6\left(2x-7\right)-12\left(x-\left(1+\frac{1}{3}x\right)\right)$$

Combine 24x and 4x to get 28x.

$$28x+3-2=6\left(2x-7\right)-12\left(x-\left(1+\frac{1}{3}x\right)\right)$$

Subtract 2 from 3 to get 1.

$$28x+1=6\left(2x-7\right)-12\left(x-\left(1+\frac{1}{3}x\right)\right)$$

Use the distributive property to multiply 6 by 2x-7.

$$28x+1=12x-42-12\left(x-\left(1+\frac{1}{3}x\right)\right)$$

To find the opposite of 1+\frac{1}{3}x, find the opposite of each term.

$$28x+1=12x-42-12\left(x-1-\frac{1}{3}x\right)$$

Combine x and -\frac{1}{3}x to get \frac{2}{3}x.

$$28x+1=12x-42-12\left(\frac{2}{3}x-1\right)$$

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

$$28x+1=12x-42-12\times \frac{2}{3}x+12$$

Express -12\times \frac{2}{3} as a single fraction.

$$28x+1=12x-42+\frac{-12\times 2}{3}x+12$$

Multiply -12 and 2 to get -24.

$$28x+1=12x-42+\frac{-24}{3}x+12$$

Divide -24 by 3 to get -8.

$$28x+1=12x-42-8x+12$$

Combine 12x and -8x to get 4x.

$$28x+1=4x-42+12$$

Add -42 and 12 to get -30.

$$28x+1=4x-30$$

Subtract 4x from both sides.

$$28x+1-4x=-30$$

Combine 28x and -4x to get 24x.

$$24x+1=-30$$

Subtract 1 from both sides.

$$24x=-30-1$$

Subtract 1 from -30 to get -31.

$$24x=-31$$

Divide both sides by 24.

$$x=\frac{-31}{24}$$

Fraction \frac{-31}{24} can be rewritten as -\frac{31}{24} by extracting the negative sign.

$$x=-\frac{31}{24}$$