To simplify the expression 2(7 - 3x) + 1/2(x - 4), we first distribute the 2 to both terms inside the parentheses and add the two terms together:

2(7 - 3x) = 14 - 6x

Now the expression becomes:

14 - 6x + 1/2(x) - 1/2(4)

We simplify further by distributing the 1/2 to both terms inside the parentheses:

14 - 6x + 1/2x - 2

Now we can combine like terms:

-6x + 1/2x = -5.5x

Therefore, the simplified expression is:

14 - 5.5x - 2 = 12 - 5.5x