Solve 1/6(8-x)+x-5/3=1/2(x+6)-x/3

$$\frac { 1 } { 6 } ( 8 - x ) + x - \frac { 5 } { 3 } = \frac { 1 } { 2 } ( x + 6 ) - \frac { x } { 3 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

$$1\left(8-x\right)+6x-10=3\left(x+6\right)-2x$$

Use the distributive property to multiply 1 by 8-x.

$$8-x+6x-10=3\left(x+6\right)-2x$$

Combine -x and 6x to get 5x.

$$8+5x-10=3\left(x+6\right)-2x$$

Subtract 10 from 8 to get -2.

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

Use the distributive property to multiply 3 by x+6.

$$-2+5x=3x+18-2x$$

Combine 3x and -2x to get x.

$$-2+5x=x+18$$

Subtract x from both sides.

$$-2+5x-x=18$$

Combine 5x and -x to get 4x.

$$-2+4x=18$$

Add 2 to both sides.

$$4x=18+2$$

Add 18 and 2 to get 20.

$$4x=20$$

Divide both sides by 4.

$$x=\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$x=5$$