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

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

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

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

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

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

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

Add 4 and 1 to get 5.

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

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

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

Use the distributive property to multiply 3 by 4x-5.

$$5-3x=12x-15$$

Subtract 12x from both sides.

$$5-3x-12x=-15$$

Combine -3x and -12x to get -15x.

$$5-15x=-15$$

Subtract 5 from both sides.

$$-15x=-15-5$$

Subtract 5 from -15 to get -20.

$$-15x=-20$$

Divide both sides by -15.

$$x=\frac{-20}{-15}$$

Reduce the fraction \frac{-20}{-15} to lowest terms by extracting and canceling out -5.

$$x=\frac{4}{3}$$