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

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)

wrong

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.

wrong again

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.

To add the given expression and express the answer in mixed number form, follow these steps:

Step 1: Simplify the fractions.
- Simplify 1/2 (x+4):
- Distribute 1/2 to both terms inside the parentheses:
1/2 * x = (1/2)x
1/2 * 4 = 2
- The expression becomes (1/2)x + 2.

- Simplify 1/4 (4x−2):
- Distribute 1/4 to both terms inside the parentheses:
1/4 * 4x = x
1/4 * -2 = -1/2
- The expression becomes x - 1/2.

Step 2: Combine like terms.
- Combine (1/2)x and x, as they have the same variable component:
- (1/2)x + x = (3/2)x

- Combine 2 and -1/2:
- 2 - 1/2 = 1 1/2

Step 3: Express the answer in mixed number form.
- Combine the whole number and the fractional part:
- 1 + 1/2 = 1 1/2

Therefore, the answer to 1/2 (x+4) + 1/4 (4x−2) in mixed number form is 1 1/2.