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

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,3,6.

$$6x+10=10\times 2x-25$$

Multiply 10 and 2 to get 20.

$$6x+10=20x-25$$

Subtract 20x from both sides.

$$6x+10-20x=-25$$

Combine 6x and -20x to get -14x.

$$-14x+10=-25$$

Subtract 10 from both sides.

$$-14x=-25-10$$

Subtract 10 from -25 to get -35.

$$-14x=-35$$

Divide both sides by -14.

$$x=\frac{-35}{-14}$$

Reduce the fraction \frac{-35}{-14} to lowest terms by extracting and canceling out -7.

$$x=\frac{5}{2}$$