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

Answer 1

To solve this problem, we need to distribute the fractions into the expressions inside the parentheses and then simplify the expression.

We start with: 1/2(x + 4) + 1/4(4x - 2)

First, we simplify 1/2(x + 4):
1/2 * x = (1/2)x
1/2 * 4 = 2
So, 1/2(x + 4) becomes (1/2)x + 2

Now, let's simplify 1/4(4x - 2):
1/4 * 4x = (1/4)(4x) = (1/4)(4/1)x = 1x = x
1/4 * -2 = (1/4)(-2) = (1/4)(-2/1) = -2/4 = -1/2
So, 1/4(4x - 2) becomes x - 1/2

Now, the expression becomes: (1/2)x + 2 + x - 1/2

To add these terms, we combine like terms:
(1/2)x + x = (1/2 + 1)x = (3/2)x
2 - 1/2 = 4/2 - 1/2 = 3/2

Finally, the simplified expression is:
(3/2)x + 3/2