Add: 1/2 (x+4) + 1/4 (4x−2) . The answer should be in mixed number form

Answer 1

To simplify the expression 1/2 (x+4) + 1/4 (4x−2), we first need to distribute the coefficients:

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

Therefore, the simplified expression is:

1/2x + 2 + x - 1/2

We can combine the like terms by adding the coefficients of x together:

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

And combining the constant terms together:

2 - 1/2 = 4/2 - 1/2 = 3/2

So the final simplified expression is:

(3/2)x + 3/2

To write this in mixed number form, we convert the improper fraction to a mixed number. The numerator of 3/2 is greater than the denominator, so we divide the numerator by the denominator:

3 ÷ 2 = 1 remainder 1

Therefore, the mixed number form of the expression is:

1 and 1/2x + 3/2