Solve 1/3(x-1)-x+1/4=x+2-3(x-3)/2

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

Solve for x

$$x = \frac{85}{7} = 12\frac{1}{7} \approx 12.142857143$$

Steps for Solving Linear Equation

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

$$4\left(x-1\right)-3\left(x+1\right)=12x+24-6\times 3\left(x-3\right)$$

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

$$4x-4-3\left(x+1\right)=12x+24-6\times 3\left(x-3\right)$$

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

$$4x-4-3x-3=12x+24-6\times 3\left(x-3\right)$$

Combine 4x and -3x to get x.

$$x-4-3=12x+24-6\times 3\left(x-3\right)$$

Subtract 3 from -4 to get -7.

$$x-7=12x+24-6\times 3\left(x-3\right)$$

Multiply -6 and 3 to get -18.

$$x-7=12x+24-18\left(x-3\right)$$

Use the distributive property to multiply -18 by x-3.

$$x-7=12x+24-18x+54$$

Combine 12x and -18x to get -6x.

$$x-7=-6x+24+54$$

Add 24 and 54 to get 78.

$$x-7=-6x+78$$

Add 6x to both sides.

$$x-7+6x=78$$

Combine x and 6x to get 7x.

$$7x-7=78$$

Add 7 to both sides.

$$7x=78+7$$

Add 78 and 7 to get 85.

$$7x=85$$

Divide both sides by 7.

$$x=\frac{85}{7}$$