Solve 2x-1/7+1-2x/6=x-1/2-18x+2/21

$$\frac { 2 x - 1 } { 7 } + \frac { 1 - 2 x } { 6 } = \frac { x - 1 } { 2 } - \frac { 18 x + 2 } { 21 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 7,6,2,21.

$$6\left(2x-1\right)+7\left(1-2x\right)=21\left(x-1\right)-2\left(18x+2\right)$$

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

$$12x-6+7\left(1-2x\right)=21\left(x-1\right)-2\left(18x+2\right)$$

Use the distributive property to multiply 7 by 1-2x.

$$12x-6+7-14x=21\left(x-1\right)-2\left(18x+2\right)$$

Add -6 and 7 to get 1.

$$12x+1-14x=21\left(x-1\right)-2\left(18x+2\right)$$

Combine 12x and -14x to get -2x.

$$-2x+1=21\left(x-1\right)-2\left(18x+2\right)$$

Use the distributive property to multiply 21 by x-1.

$$-2x+1=21x-21-2\left(18x+2\right)$$

Use the distributive property to multiply -2 by 18x+2.

$$-2x+1=21x-21-36x-4$$

Combine 21x and -36x to get -15x.

$$-2x+1=-15x-21-4$$

Subtract 4 from -21 to get -25.

$$-2x+1=-15x-25$$

Add 15x to both sides.

$$-2x+1+15x=-25$$

Combine -2x and 15x to get 13x.

$$13x+1=-25$$

Subtract 1 from both sides.

$$13x=-25-1$$

Subtract 1 from -25 to get -26.

$$13x=-26$$

Divide both sides by 13.

$$x=\frac{-26}{13}$$

Divide -26 by 13 to get -2.

$$x=-2$$