Solve 2(2-x)/2+(x-1)/3+1=4left(x-2right)/2

$$2 \frac{ (2-x) }{ 2 } + \frac{ (x-1) }{ 3 } +1 = \frac{ 4 \left( x-2 \right) }{ 2 }$$

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 6, the least common multiple of 2,3.

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

Use the distributive property to multiply 6 by 2-x.

$$12-6x+2\left(x-1\right)+6=3\times 4\left(x-2\right)$$

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

$$12-6x+2x-2+6=3\times 4\left(x-2\right)$$

Combine -6x and 2x to get -4x.

$$12-4x-2+6=3\times 4\left(x-2\right)$$

Subtract 2 from 12 to get 10.

$$10-4x+6=3\times 4\left(x-2\right)$$

Add 10 and 6 to get 16.

$$16-4x=3\times 4\left(x-2\right)$$

Multiply 3 and 4 to get 12.

$$16-4x=12\left(x-2\right)$$

Use the distributive property to multiply 12 by x-2.

$$16-4x=12x-24$$

Subtract 12x from both sides.

$$16-4x-12x=-24$$

Combine -4x and -12x to get -16x.

$$16-16x=-24$$

Subtract 16 from both sides.

$$-16x=-24-16$$

Subtract 16 from -24 to get -40.

$$-16x=-40$$

Divide both sides by -16.

$$x=\frac{-40}{-16}$$

Reduce the fraction \frac{-40}{-16} to lowest terms by extracting and canceling out -8.

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