Solve 2-x/2+3-2x/11=x+1/3+5

$$\frac { 2 - x } { 2 } + \frac { 3 - 2 x } { 11 } = \frac { x + 1 } { 3 } + 5$$

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 66, the least common multiple of 2,11,3.

$$33\left(2-x\right)+6\left(3-2x\right)=22\left(x+1\right)+330$$

Use the distributive property to multiply 33 by 2-x.

$$66-33x+6\left(3-2x\right)=22\left(x+1\right)+330$$

Use the distributive property to multiply 6 by 3-2x.

$$66-33x+18-12x=22\left(x+1\right)+330$$

Add 66 and 18 to get 84.

$$84-33x-12x=22\left(x+1\right)+330$$

Combine -33x and -12x to get -45x.

$$84-45x=22\left(x+1\right)+330$$

Use the distributive property to multiply 22 by x+1.

$$84-45x=22x+22+330$$

Add 22 and 330 to get 352.

$$84-45x=22x+352$$

Subtract 22x from both sides.

$$84-45x-22x=352$$

Combine -45x and -22x to get -67x.

$$84-67x=352$$

Subtract 84 from both sides.

$$-67x=352-84$$

Subtract 84 from 352 to get 268.

$$-67x=268$$

Divide both sides by -67.

$$x=\frac{268}{-67}$$

Divide 268 by -67 to get -4.

$$x=-4$$