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

To simplify the expression 1/2(x+4) + 1/4(4x-2), we will first distribute the coefficients inside the parentheses:

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

Next, we can simplify each term:

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

Simplifying further:

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

To multiply a fraction by a whole number, we multiply the numerator by the whole number while keeping the denominator the same:

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

The denominators of all the fractions are the same, so we can now combine like terms:

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

The fractions (4/4)x and (2/4) can be simplified further:

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

To add/subtract fractions, we need to have a common denominator. In this case, the common denominator is 2:

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

Combining like terms:

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

To subtract a fraction, we need a common denominator of 2:

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

Simplifying:

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

Combining like terms:

(3/2)x + 1/2

Therefore, 1/2(x+4) + 1/4(4x-2) simplifies to (3/2)x + 1/2.