add:%2012(x+4)+14(4x%E2%88%922)%20.%20Answer%20should%20be%20in%20mixed%20number%20form.

Let's simplify the expression step by step:

Given the expression: \[ 2012(x + 4) + 14(4x - 2) \]

1. Distribute the 2012 and the 14: \[ 2012(x) + 2012(4) + 14(4x) - 14(2) \] This simplifies to: \[ 2012x + 8048 + 56x - 28 \]

2. Combine like terms:

   • Combine the \(x\) terms: \[ 2012x + 56x = (2012 + 56)x = 2068x \]
   • Combine the constant terms: \[ 8048 - 28 = 8020 \]

So, the expression simplifies to: \[ 2068x + 8020 \]

If you're looking for this in a mixed number form, consider \(8020\) can be written as \(8020\) (since it is already an integer with no fractional part).

Thus, the simplified expression is: \[ 2068x + 8020 \]

If there's a specific part of the expression you'd like to convert to mixed number format further, please clarify!

Let's simplify the expression step-by-step:

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

1. Distribute the fractions: \[ \frac{1}{2} \cdot x + \frac{1}{2} \cdot 4 + \frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 \] This expands to: \[ \frac{1}{2}x + 2 + x - \frac{1}{2} \]

2. Now, combine like terms:

   • First, let's convert the mixed numbers to have a common denominator. \(2\) can be converted to \(\frac{4}{2}\): \[ \frac{1}{2}x + \frac{4}{2} - \frac{1}{2} + x \]

3. Combine the \(x\) terms and constants:

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

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

So, the expression simplifies to: \[ \frac{3}{2}x + \frac{3}{2} \]

4. To write this in mixed number form:

• The coefficients \(\frac{3}{2}\) can be written as \(1\frac{1}{2}\) (because \(\frac{3}{2} = 1 + \frac{1}{2}\)).

Thus, the final answer in mixed number form is: \[ 1\frac{1}{2}x + 1\frac{1}{2} \]

If you need the answer in a specific form, please let me know!

The final simplified expression is:

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

In mixed number form, this can be expressed as:

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

So the answers for each term in mixed number form are:

1. The \(x\) term: \(1\frac{1}{2}x\)
2. The constant term: \(1\frac{1}{2}\)

Therefore, the complete answer can be presented as:

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

If you need any further clarification or assistance, feel free to ask!

Let's carefully recalculate the expression step by step:

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

Step 1: Distribute the fractions

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

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

Step 2: Combining the results

Now, we can combine the two results: \[ \frac{1}{2}x + 2 + x - \frac{1}{2} \]

Step 3: Combine like terms

1. Combine the \(x\) terms:

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

2. Combine the constant terms:

   • \(2 - \frac{1}{2}\): \[ 2 = \frac{4}{2} \quad \text{ so, } \quad \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \]

Final Result

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

Step 4: Convert to Mixed Number Form

Now, let's convert each coefficient to mixed number form:

• \(\frac{3}{2}x\) can be expressed as \(1\frac{1}{2}x\)
• \(\frac{3}{2}\) can be expressed as \(1\frac{1}{2}\)

Thus, the final expression in mixed number form is: \[ 1\frac{1}{2}x + 1\frac{1}{2} \]

I apologize for any confusion earlier. If there are any specific parts of the answer that you believe are incorrect or if you want to evaluate a different aspect, please let me know!

No problem! Please take your time to check. I'm here if you have any questions or if you need any further assistance with the calculations. Just let me know!

Let’s work through the expression again step by step to ensure we have the correct answer.

We start with: \[ \frac{1}{2} (x + 4) + \frac{1}{4} (4x - 2) \]

Step 1: Distribute the fractions

1. Distributing \(\frac{1}{2}\): \[ \frac{1}{2}(x) + \frac{1}{2}(4) = \frac{1}{2}x + 2 \]

2. Distributing \(\frac{1}{4}\): \[ \frac{1}{4}(4x) - \frac{1}{4}(2) = x - \frac{1}{2} \]

Step 2: Combine like terms

Now, we combine the results: \[ \frac{1}{2}x + 2 + x - \frac{1}{2} \]

Combining:

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

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

Final Result

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

Convert to Mixed Number Form

In mixed number format:

• \(\frac{3}{2}x\) is \(1\frac{1}{2}x\)
• \(\frac{3}{2}\) is \(1\frac{1}{2}\)

Thus, the final expression in mixed number form is: \[ 1\frac{1}{2}x + 1\frac{1}{2} \]

Conclusion

The calculations are indeed correct. The answer, expressed in mixed number form, is: \[ 1\frac{1}{2}x + 1\frac{1}{2} \]

Please let me know if you need any further clarification or assistance!