Add: 1/2(x+4)+1/4(4x-2). Answer should be in mixed number form

Answer 1

To simplify the expression, let's first distribute the fractions:

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

Simplifying each term:
= 1/2x + 2/2 + 4/4x - 2/4

Next, let's find a common denominator for the fractions, which is 4:

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

= (2/4)x + 2/2 + (16/16)x - 2/4

Simplifying the mixed numbers:

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

Now combine like terms:

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

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

The final answer in mixed number form is:

= 1 (1/2) + (1/2)