Solve x+1/2+2x-1/3=x-2/4+3x-5/6

$$\frac { x + 1 } { 2 } + \frac { 2 x - 1 } { 3 } = \frac { x - 2 } { 4 } + \frac { 3 x - 5 } { 6 }$$

Solve for x

$$x = -\frac{18}{5} = -3\frac{3}{5} = -3.6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4,6.

$$6\left(x+1\right)+4\left(2x-1\right)=3\left(x-2\right)+2\left(3x-5\right)$$

Use the distributive property to multiply 6 by x+1.

$$6x+6+4\left(2x-1\right)=3\left(x-2\right)+2\left(3x-5\right)$$

Use the distributive property to multiply 4 by 2x-1.

$$6x+6+8x-4=3\left(x-2\right)+2\left(3x-5\right)$$

Combine 6x and 8x to get 14x.

$$14x+6-4=3\left(x-2\right)+2\left(3x-5\right)$$

Subtract 4 from 6 to get 2.

$$14x+2=3\left(x-2\right)+2\left(3x-5\right)$$

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

$$14x+2=3x-6+2\left(3x-5\right)$$

Use the distributive property to multiply 2 by 3x-5.

$$14x+2=3x-6+6x-10$$

Combine 3x and 6x to get 9x.

$$14x+2=9x-6-10$$

Subtract 10 from -6 to get -16.

$$14x+2=9x-16$$

Subtract 9x from both sides.

$$14x+2-9x=-16$$

Combine 14x and -9x to get 5x.

$$5x+2=-16$$

Subtract 2 from both sides.

$$5x=-16-2$$

Subtract 2 from -16 to get -18.

$$5x=-18$$

Divide both sides by 5.

$$x=\frac{-18}{5}$$

Fraction \frac{-18}{5} can be rewritten as -\frac{18}{5} by extracting the negative sign.

$$x=-\frac{18}{5}$$