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

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

Solve for x

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

Steps for Solving Linear Equation

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

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

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

$$1-3x=2x-10$$

Subtract 2x from both sides.

$$1-3x-2x=-10$$

Combine -3x and -2x to get -5x.

$$1-5x=-10$$

Subtract 1 from both sides.

$$-5x=-10-1$$

Subtract 1 from -10 to get -11.

$$-5x=-11$$

Divide both sides by -5.

$$x=\frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{11}{5}$$