Solve 1/2+x/9-2(3x-2)/9=1-x/6

$$\frac { 1 } { 2 } + \frac { x } { 9 } - \frac { 2 ( 3 x - 2 ) } { 9 } = 1 - \frac { x } { 6 }$$

Solve for x

$$x=-\frac{1}{7}\approx -0.142857143$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 2,9,6.

$$9+2x-2\times 2\left(3x-2\right)=18-3x$$

Multiply -2 and 2 to get -4.

$$9+2x-4\left(3x-2\right)=18-3x$$

Use the distributive property to multiply -4 by 3x-2.

$$9+2x-12x+8=18-3x$$

Combine 2x and -12x to get -10x.

$$9-10x+8=18-3x$$

Add 9 and 8 to get 17.

$$17-10x=18-3x$$

Add 3x to both sides.

$$17-10x+3x=18$$

Combine -10x and 3x to get -7x.

$$17-7x=18$$

Subtract 17 from both sides.

$$-7x=18-17$$

Subtract 17 from 18 to get 1.

$$-7x=1$$

Divide both sides by -7.

$$x=\frac{1}{-7}$$

Fraction \frac{1}{-7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$x=-\frac{1}{7}$$