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To simplify the expression, we must distribute the fractions and combine like terms:
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
Now, let's combine like terms:
= (1/2)x + x + (1/2) - 1
= (1/2 + 1)x + (1/2 - 1)
= (3/2)x - 1/2