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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

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

$$3x-15+6x=2\times 2x-5$$

Combine 3x and 6x to get 9x.

$$9x-15=2\times 2x-5$$

Multiply 2 and 2 to get 4.

$$9x-15=4x-5$$

Subtract 4x from both sides.

$$9x-15-4x=-5$$

Combine 9x and -4x to get 5x.

$$5x-15=-5$$

Add 15 to both sides.

$$5x=-5+15$$

Add -5 and 15 to get 10.

$$5x=10$$

Divide both sides by 5.

$$x=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$x=2$$