Solve x+5/6+2x/3=1-x/2+1

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

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 2 to get 4.

$$x+5+4x=3\left(1-x\right)+6$$

Combine x and 4x to get 5x.

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

Use the distributive property to multiply 3 by 1-x.

$$5x+5=3-3x+6$$

Add 3 and 6 to get 9.

$$5x+5=9-3x$$

Add 3x to both sides.

$$5x+5+3x=9$$

Combine 5x and 3x to get 8x.

$$8x+5=9$$

Subtract 5 from both sides.

$$8x=9-5$$

Subtract 5 from 9 to get 4.

$$8x=4$$

Divide both sides by 8.

$$x=\frac{4}{8}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{1}{2}$$