Solve 2(3x-1)/2+1/4x=2+5(x-2)/6+1/12x

$$\frac { 2 ( 3 x - 1 ) } { 2 } + \frac { 1 } { 4 } x = 2 + \frac { 5 ( x - 2 ) } { 6 } + \frac { 1 } { 12 } x$$

Solve for x

$$x=\frac{4}{7}\approx 0.571428571$$

Steps for Solving Linear Equation

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

$$6\times 2\left(3x-1\right)+3x=24+2\times 5\left(x-2\right)+1x$$

Multiply 6 and 2 to get 12.

$$12\left(3x-1\right)+3x=24+2\times 5\left(x-2\right)+1x$$

Use the distributive property to multiply 12 by 3x-1.

$$36x-12+3x=24+2\times 5\left(x-2\right)+1x$$

Combine 36x and 3x to get 39x.

$$39x-12=24+2\times 5\left(x-2\right)+1x$$

Multiply 2 and 5 to get 10.

$$39x-12=24+10\left(x-2\right)+1x$$

Use the distributive property to multiply 10 by x-2.

$$39x-12=24+10x-20+1x$$

Subtract 20 from 24 to get 4.

$$39x-12=4+10x+1x$$

Combine 10x and 1x to get 11x.

$$39x-12=4+11x$$

Subtract 11x from both sides.

$$39x-12-11x=4$$

Combine 39x and -11x to get 28x.

$$28x-12=4$$

Add 12 to both sides.

$$28x=4+12$$

Add 4 and 12 to get 16.

$$28x=16$$

Divide both sides by 28.

$$x=\frac{16}{28}$$

Reduce the fraction \frac{16}{28} to lowest terms by extracting and canceling out 4.

$$x=\frac{4}{7}$$