Add: 1/2(x+4)+1/4(4x−2)

Answer 1

To add the expressions 1/2(x+4) and 1/4(4x-2), we can first simplify each term separately and then combine them.

First, let's simplify 1/2(x+4):
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2

Next, let's simplify 1/4(4x-2):
1/4(4x-2) = 1/4 * 4x + 1/4 * (-2) = x - 1/2

Now, let's combine the simplified expressions:
(1/2x + 2) + (x - 1/2)

To add the terms, we need a common denominator, which in this case is 2. Therefore, we can rewrite the expression as:
(1/2x + 4/2) + (2x/2 - 1/2)

Now, combine like terms:
1/2x + 4/2 + 2x/2 - 1/2 = (1/2x + 2x/2) + (4/2 - 1/2) = (1/2x + x) + (3/2)

Finally, combine the like terms:
(3/2)x + (3/2) = (3/2)(x+1)

So, the simplified sum of 1/2(x+4) + 1/4(4x-2) is (3/2)(x+1).