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

Answer 1

To add the two fractions \( \frac{1}{2} (x + 4) \) and \( \frac{1}{4} (4x - 2) \), we first simplify each term.

1. Start with the first term: \[ \frac{1}{2} (x + 4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2 \]

2. Now, simplify the second term: \[ \frac{1}{4} (4x - 2) = \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2} \]

Now we can combine the two terms: \[ \left( \frac{1}{2}x + 2 \right) + \left( x - \frac{1}{2} \right) \]

Combine like terms:

• The \( x \) terms: \[ \frac{1}{2}x + x = \frac{1}{2}x + \frac{2}{2}x = \frac{3}{2}x \]

• The constant terms: \[ 2 - \frac{1}{2} = 2 - 0.5 = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \]

Putting it all together, we have: \[ \frac{3}{2}x + \frac{3}{2} \]

To express this in mixed form, we can factor out \( \frac{3}{2} \): \[ \frac{3}{2}(x + 1) \]

Thus, the sum \( \frac{1}{2} (x + 4) + \frac{1}{4} (4x - 2) \) in mixed form is: \[ \frac{3}{2}(x + 1) \]

Answer 2

it says you are very wrong

Answer 3

I apologize for any confusion in my previous response. Let's go through the calculation step by step to ensure accuracy:

We need to add: \[ \frac{1}{2} (x + 4) + \frac{1}{4} (4x - 2) \]

Step 1: Distribute the fractions

1. For the first term: \[ \frac{1}{2} (x + 4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2 \]

2. For the second term: \[ \frac{1}{4} (4x - 2) = \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2} \]

Step 2: Combine the two expressions

Now we have: \[ \left( \frac{1}{2}x + 2 \right) + \left( x - \frac{1}{2} \right) \]

Combine like terms:

• The \(x\) terms: \[ \frac{1}{2}x + x = \frac{1}{2}x + \frac{2}{2}x = \frac{3}{2}x \]

• The constant terms: \[ 2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{3}{2} \]

Step 3: Combine everything together

So we get: \[ \frac{3}{2}x + \frac{3}{2} \]

Step 4: Put in mixed form

We can factor out \( \frac{3}{2} \): \[ \frac{3}{2}(x + 1) \]

So the final result in a simple form is: \[ \frac{3}{2}x + \frac{3}{2} \] And if you want to express \( \frac{3}{2} \) as a mixed number, it's \( 1 \frac{1}{2} \).

If you require the answer as a mixed fraction in terms of numbers: \[ \frac{3}{2}x + 1 \frac{1}{2} \]

Please let me know how you'd like it formatted! If there is a specific error I need to address, I’d be happy to help clarify!

Answer 4

youre still wrong it says

Answer 5

I apologize for the confusion and appreciate your patience. Let's carefully go through the addition of the expressions step by step to find the correct answer:

We want to add:

\[ \frac{1}{2} (x + 4) + \frac{1}{4} (4x - 2) \]

Step 1: Distribute the fractions

1. For the first term: \[ \frac{1}{2}(x + 4) = \frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2 \]

2. For the second term: \[ \frac{1}{4}(4x - 2) = \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2} \]

Step 2: Combine the terms

Now combine both results:

\[ \left(\frac{1}{2}x + 2\right) + \left(x - \frac{1}{2}\right) \]

Combining \(x\) terms:

• Convert \(x\) to \(\frac{2}{2}x\) for easy addition: \[ \frac{1}{2}x + \frac{2}{2}x = \frac{3}{2}x \]

Now combine constant terms: \[ 2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \]

Step 3: Combine everything together

Putting it all together: \[ \frac{3}{2}x + \frac{3}{2} \]

Step 4: Convert to mixed form

The expression can be factored: \[ \frac{3}{2} (x + 1) \]

Alternatively, in mixed number format, \(\frac{3}{2}\) can be expressed as \(1 \frac{1}{2}\):

Thus, the final result in mixed form is: \[ 1 \frac{1}{2} (x + 1) \]

Final Answer

So the final combined result in mixed form is:

\[ \frac{3}{2}x + 1 \frac{1}{2} \]

If you have specific conditions you've noted that led to errors, please let me know, and I'll correct those issues immediately. Thank you for your understanding!