Solve 5x-7/3-1-x/2=5-x/6+3x-2/4

$$\frac { 5 x - 7 } { 3 } - \frac { 1 - x } { 2 } = \frac { 5 - x } { 6 } + \frac { 3 x - 2 } { 4 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$4\left(5x-7\right)-6\left(1-x\right)=2\left(5-x\right)+3\left(3x-2\right)$$

Use the distributive property to multiply 4 by 5x-7.

$$20x-28-6\left(1-x\right)=2\left(5-x\right)+3\left(3x-2\right)$$

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

$$20x-28-6+6x=2\left(5-x\right)+3\left(3x-2\right)$$

Subtract 6 from -28 to get -34.

$$20x-34+6x=2\left(5-x\right)+3\left(3x-2\right)$$

Combine 20x and 6x to get 26x.

$$26x-34=2\left(5-x\right)+3\left(3x-2\right)$$

Use the distributive property to multiply 2 by 5-x.

$$26x-34=10-2x+3\left(3x-2\right)$$

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

$$26x-34=10-2x+9x-6$$

Combine -2x and 9x to get 7x.

$$26x-34=10+7x-6$$

Subtract 6 from 10 to get 4.

$$26x-34=4+7x$$

Subtract 7x from both sides.

$$26x-34-7x=4$$

Combine 26x and -7x to get 19x.

$$19x-34=4$$

Add 34 to both sides.

$$19x=4+34$$

Add 4 and 34 to get 38.

$$19x=38$$

Divide both sides by 19.

$$x=\frac{38}{19}$$

Divide 38 by 19 to get 2.

$$x=2$$