1/2(x+4)+1/4(4x−2)

To simplify 1/2(x+4)+1/4(4x−2), we can distribute the fractions:

1/2(x+4) + 1/4(4x-2)
= (1/2)x + (1/2)(4) + (1/4)(4x) - (1/4)(2)
= (1/2)x + 2/2 + (4/4)x - 2/4
= (1/2)x + 1 + x - 1/2
= (1/2)x + x + 1 - 1/2
= (1/2 + 1)x + 1/2
= (3/2)x + 1/2

So, 1/2(x+4)+1/4(4x−2) simplifies to (3/2)x + 1/2.