Add: 1/2(x+4)+1/4(4x−2)

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

First, simplify each fraction by multiplying the numerator and denominator by the least common multiple of the denominators.

For 1/2(x+4):

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

For 1/4(4x-2):

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

Now, our expression becomes:

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

Combine like terms:

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

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

(3/2)x + 3/2

Simplifying the expression further, we can multiply both the numerator and denominator by 2 to get rid of the fractions:

2 * (3/2)x + 2 * (3/2)

(6/2)x + 6/2

3x + 3

Therefore, the simplified expression is 3x + 3.

thats not right

Apologies for the incorrect simplification. Let's try again.

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

First, distribute the fractions:

1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2

Simplify each term:

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

Combine like terms:

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

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

To simplify, we can multiply each term by 2 to get rid of fractions:

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

3x + 1

Therefore, the simplified expression is 3x + 1.

wrong

Apologies for the misunderstanding. Let's try again.

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

Distribute the fractions:

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

Simplify each term:

1/2x + 2/2 + 4/4x - 2/4

Combine like terms:

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

Simplify further:

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

Now, find a common denominator for each fraction:

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

Combine the fractions:

(3/2)x + (3/2)

Therefore, the simplified expression is (3/2)x + (3/2).