1/2(x+4) + 1/4(4x-2)

To simplify the expression 1/2(x+4) + 1/4(4x-2), we need to distribute and combine like terms.

First, distribute 1/2 to (x+4):

1/2(x+4) = 1/2 * x + 1/2 * 4
= 1/2x + 2

Next, distribute 1/4 to (4x-2):

1/4(4x-2) = 1/4 * 4x + 1/4 * (-2)
= x - 1/2

Now we can combine the terms:

1/2x + 2 + x - 1/2

To combine the terms, we need to have the same denominator:

1/2x + x + 2 - 1/2

Now we can rewrite 1/2x as 2/4x to get the common denominator:

2/4x + x + 2 - 1/2

Combining the terms:

(2/4x + 1x) + 2 - 1/2

Now, we can simplify and combine like terms:

(2x/4x) + 1x + 2 - 1/2
= 1/2 + x + 2 - 1/2

Combine the constant terms:

1/2 + 2 - 1/2 = 2 + 1/2 - 1/2

Simplify:

2 + 1/2 - 1/2 = 2

Therefore, the simplified expression is 2.