Solve 11x+3/11+x-1/2+3(x-3)/22=3/11-frac{2(x+1)}{11}

$$\frac { 11 x + 3 } { 11 } + \frac { x - 1 } { 2 } + \frac { 3 ( x - 3 ) } { 22 } = \frac { 3 } { 11 } - \frac { 2 ( x + 1 ) } { 11 }$$

Solve for x

$$x=\frac{2}{5}=0.4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 22, the least common multiple of 11,2,22.

$$2\left(11x+3\right)+11\left(x-1\right)+3\left(x-3\right)=6-2\times 2\left(x+1\right)$$

Use the distributive property to multiply 2 by 11x+3.

$$22x+6+11\left(x-1\right)+3\left(x-3\right)=6-2\times 2\left(x+1\right)$$

Use the distributive property to multiply 11 by x-1.

$$22x+6+11x-11+3\left(x-3\right)=6-2\times 2\left(x+1\right)$$

Combine 22x and 11x to get 33x.

$$33x+6-11+3\left(x-3\right)=6-2\times 2\left(x+1\right)$$

Subtract 11 from 6 to get -5.

$$33x-5+3\left(x-3\right)=6-2\times 2\left(x+1\right)$$

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

$$33x-5+3x-9=6-2\times 2\left(x+1\right)$$

Combine 33x and 3x to get 36x.

$$36x-5-9=6-2\times 2\left(x+1\right)$$

Subtract 9 from -5 to get -14.

$$36x-14=6-2\times 2\left(x+1\right)$$

Multiply -2 and 2 to get -4.

$$36x-14=6-4\left(x+1\right)$$

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

$$36x-14=6-4x-4$$

Subtract 4 from 6 to get 2.

$$36x-14=2-4x$$

Add 4x to both sides.

$$36x-14+4x=2$$

Combine 36x and 4x to get 40x.

$$40x-14=2$$

Add 14 to both sides.

$$40x=2+14$$

Add 2 and 14 to get 16.

$$40x=16$$

Divide both sides by 40.

$$x=\frac{16}{40}$$

Reduce the fraction \frac{16}{40} to lowest terms by extracting and canceling out 8.

$$x=\frac{2}{5}$$