Question
add:%2012(x+4)+14(4x%E2%88%922)%20.%20Answer%20should%20be%20in%20mixed%20number%20form.
Answers
GPT-4o mini
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!
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!
Hawt Chikin nuggies
add:
1/2 (x+4) + 1/4 (4x-2). Answer should be in a mixed number form.
1/2 (x+4) + 1/4 (4x-2). Answer should be in a mixed number form.
GPT-4o mini
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!
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!
Hawt Chikin nuggies
So what’s the answer
GPT-4o mini
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!
\[
\frac{3}{2}x + \frac{3}{2}
\]
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!
Hawt Chikin nuggies
Incorrect
GPT-4o mini
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!
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!
Hawt Chikin nuggies
Wait actually let me check again
GPT-4o mini
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!
Hawt Chikin nuggies
Can someone give the answers please or tell me if the bot is correct please 🙏
GPT-4o mini
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!
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!