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

Answer 1

To add the fractions 1/2 (x+4) and 1/4 (4x - ), we need to find a common denominator first.

The common denominator of the fractions 1/2 and 1/4 is 4.

So, we can rewrite the given fractions with 4 as the denominator:

1/2 (x+4) = (2/2)(x+4) = 2(x+4)/4 = (2x+8)/4

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

Now, we can add the fractions:

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

Since the denominators are the same, we can add the numerators:

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

Combining like terms:

(6x + 8)/4

Now, we can simplify the fraction:

(6x + 8)/4 = 6x/4 + 8/4 = 3x/2 + 2

The final answer in mixed number form is 3x/2 + 2.

Answer 2

that's wrong

Answer 3

I apologize for the mistake. Let's try again.

We have 1/2 (x+4) + 1/4 (4x - ).

To find a common denominator, we need to find the least common multiple (LCM) of 2 and 4, which is 4.

So, let's rewrite the fractions with a denominator of 4:

1/2 (x+4) = (2/2)(x+4) = 2(x+4)/4 = (2x+8)/4

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

Now, we can add the fractions:

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

Since the denominators are the same, we can add the numerators:

(2x+8 + 4x - )/4 = (6x + 8)/4

We can simplify this fraction by dividing both the numerator and denominator by 2:

(6x + 8)/4 = (3x + 4)/2

Therefore, the answer in mixed number form is 3x/2 + 4/2, which simplifies to 3x/2 + 2.

I apologize for the confusion earlier. The correct answer is 3x/2 + 2.