Solve 2/3+7-x/6+7/6-x+1/2=frac{2}{9}(1-x)+frac{11}{6}

$$\frac { 2 } { 3 } + \frac { 7 - x } { 6 } + \frac { 7 } { 6 } - \frac { x + 1 } { 2 } = \frac { 2 } { 9 } ( 1 - x ) + \frac { 11 } { 6 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 3,6,2,9.

$$12+3\left(7-x\right)+21-9\left(x+1\right)=4\left(1-x\right)+33$$

Use the distributive property to multiply 3 by 7-x.

$$12+21-3x+21-9\left(x+1\right)=4\left(1-x\right)+33$$

Add 12 and 21 to get 33.

$$33-3x+21-9\left(x+1\right)=4\left(1-x\right)+33$$

Add 33 and 21 to get 54.

$$54-3x-9\left(x+1\right)=4\left(1-x\right)+33$$

Use the distributive property to multiply -9 by x+1.

$$54-3x-9x-9=4\left(1-x\right)+33$$

Combine -3x and -9x to get -12x.

$$54-12x-9=4\left(1-x\right)+33$$

Subtract 9 from 54 to get 45.

$$45-12x=4\left(1-x\right)+33$$

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

$$45-12x=4-4x+33$$

Add 4 and 33 to get 37.

$$45-12x=37-4x$$

Add 4x to both sides.

$$45-12x+4x=37$$

Combine -12x and 4x to get -8x.

$$45-8x=37$$

Subtract 45 from both sides.

$$-8x=37-45$$

Subtract 45 from 37 to get -8.

$$-8x=-8$$

Divide both sides by -8.

$$x=\frac{-8}{-8}$$

Divide -8 by -8 to get 1.

$$x=1$$