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

To simplify the expression 1/2(x+4) + 1/4(4x -2), let's start by multiplying out the terms:

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

Now, simplify each term:

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

Now, combine like terms:

x/2 + 2 + x - 1/2

To simplify further, find a common denominator for the fractions:

(2/2)(x/2) + (4/2)(2/2) + (2/2)(x) - (1/2)(1/2)
= 2x/4 + 8/4 + 2x/2 - 1/4

Now, combine like terms:

2x/4 + 8/4 + 2x/2 - 1/4
= (2x + 8 + 4x - 1)/4
= (6x + 7)/4

Therefore, 1/2(x+4) + 1/4(4x -2) simplifies to (6x + 7)/4.