Solve -2(x-3)/9+7/18-x-2/6=x-x-2/3-frac{3(x+1)}{2}

$$- \frac { 2 ( x - 3 ) } { 9 } + \frac { 7 } { 18 } - \frac { x - 2 } { 6 } = x - \frac { x - 2 } { 3 } - \frac { 3 ( x + 1 ) } { 2 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

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

$$-2\times 2\left(x-3\right)+7-3\left(x-2\right)=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

Multiply -2 and 2 to get -4.

$$-4\left(x-3\right)+7-3\left(x-2\right)=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

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

$$-4x+12+7-3\left(x-2\right)=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

Add 12 and 7 to get 19.

$$-4x+19-3\left(x-2\right)=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

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

$$-4x+19-3x+6=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

Combine -4x and -3x to get -7x.

$$-7x+19+6=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

Add 19 and 6 to get 25.

$$-7x+25=18x-6\left(x-2\right)-9\times 3\left(x+1\right)$$

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

$$-7x+25=18x-6x+12-9\times 3\left(x+1\right)$$

Combine 18x and -6x to get 12x.

$$-7x+25=12x+12-9\times 3\left(x+1\right)$$

Multiply -9 and 3 to get -27.

$$-7x+25=12x+12-27\left(x+1\right)$$

Use the distributive property to multiply -27 by x+1.

$$-7x+25=12x+12-27x-27$$

Combine 12x and -27x to get -15x.

$$-7x+25=-15x+12-27$$

Subtract 27 from 12 to get -15.

$$-7x+25=-15x-15$$

Add 15x to both sides.

$$-7x+25+15x=-15$$

Combine -7x and 15x to get 8x.

$$8x+25=-15$$

Subtract 25 from both sides.

$$8x=-15-25$$

Subtract 25 from -15 to get -40.

$$8x=-40$$

Divide both sides by 8.

$$x=\frac{-40}{8}$$

Divide -40 by 8 to get -5.

$$x=-5$$