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

Answer 1

To simplify the given expression, let's start by finding a common denominator for the fractions:

The least common multiple of 2 and 4 is 4.
1/2(x+4) can be written as 2/4(x+4)
1/4(4x-2) remains the same.

Now, let's simplify the expression:

2/4(x+4) + 1/4(4x−2) can be written as (2(x+4) + 1(4x−2))/4

Distributing the terms:

(2x + 8 + 4x - 2)/4

Combining like terms:

(6x + 6)/4

Now, to express the solution in mixed number form, we can divide the numerator by the denominator:

6x/4 + 6/4 = 3x/2 + 3/2

Therefore, the expression 1/2(x+4) + 1/4(4x−2) simplifies to the mixed number form 3x/2 + 3/2.

Answer 2

wrong the answer is 1 1/2x+1 1/2

Answer 3

Apologies for the mistake. Let's re-evaluate the expression correctly:

To simplify the given expression, let's start by finding a common denominator for the fractions:

The least common multiple of 2 and 4 is 4.
1/2(x+4) can be written as 2/4(x+4)
1/4(4x-2) can be written as 1/4(4x-2)

Now, let's simplify the expression:

2/4(x+4) + 1/4(4x-2) can be written as (2(x+4) + 1(4x-2))/4

Distributing the terms:

(2x + 8 + 4x - 2)/4

Combining like terms:

(6x + 6)/4

Now, let's divide the numerator by the denominator:

(6x + 6)/4 = (6/4)x + (6/4)

Simplifying further:

(6/4)x + (6/4) = (3/2)x + (3/2)

This expression can be further simplified to the mixed number form:

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

Therefore, the expression 1/2(x+4) + 1/4(4x−2) simplifies to 1 1/2x + 1 1/2.