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

Question

Put it as a mixed number

Answer 1

To add the two fractions, we first need to find a common denominator. The common denominator for 2 and 4 is 4. So, we can rewrite the fractions as follows:

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

Now we can add the fractions:

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

Combining the x terms, we have:

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

Simplifying the fractions, we get:

6/4 x + 4/4

Now, we can separate the whole number part and the fractional part:

6/4 x can be simplified to 3/2 x, and 4/4 can be simplified to 1. So, the final answer is:

3/2 x + 1 (in mixed number form)

Answer 2

wrong

Answer 3

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

To add the fractions, 1/2 (x+4) and 1/4 (4x−2), we need to find a common denominator. The least common denominator for 2 and 4 is 4.

1/2 (x+4) = 2/4 (x+4) (multiplying numerator and denominator by 2)
1/4 (4x−2) = 1/4 * 1 * (4x−2) = 4/4 x - 1/4 * 2 = 4/4 x - 1/2

Now we can add the fractions:

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

Combining the x terms, we have:

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

Simplifying the fractions, we get:

6/4 x + 8/4

Now, we can simplify the mixed number:

6/4 x + 8/4 = 1 1/2 x + 2

Therefore, the answer in mixed number form is 1 1/2 x + 2.

Answer 4

wrong again

Answer 5

I apologize for the mistake. Let's solve it again.

To add the fractions, 1/2 (x+4) and 1/4 (4x−2), we need to find a common denominator. The least common denominator for 2 and 4 is 4.

1/2 (x+4) = 2/4 (x+4) (multiplying numerator and denominator by 2)
1/4 (4x−2) = 1/4 * 1 * (4x−2) = 4/4 x - 1/4 * 2 = 4/4 x - 1/2

Now we can add the fractions:

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

Combining the x terms, we have:

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

Simplifying the fractions, we get:

6/4 x + 8/4

Now, let's simplify the mixed number:

6/4 x + 8/4 = 1 2/4 x + 2

Since 2/4 can be simplified to 1/2, we get:

1 2/4 x + 2 = 1 1/2 x + 2

Therefore, the correct answer in mixed number form is 1 1/2 x + 2.