Question

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

Answer 1

no

Answer 2

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

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

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

Now, we can add the two results together:
\[
\left( \frac{1}{2} x + 2 \right) + \left( x - \frac{1}{2} \right)
\]

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:
\[
2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{3}{2}
\]

Therefore, the combined result is:
\[
\frac{3}{2} x + \frac{3}{2}
\]

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

Thus, the final answer is:
\[
\frac{3}{2} ( x + 1 )
\]

Answer 3

Apologies for any confusion in my previous response. Let's go through the problem step-by-step again and find the correct answer.

We want to simplify the expression:

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

1. **Distribute** the terms in the parentheses:
- For \( \frac{1}{2}(x + 4) \):
\[
\frac{1}{2}x + \frac{1}{2} \cdot 4 = \frac{1}{2}x + 2
\]
- For \( \frac{1}{4}(4x - 2) \):
\[
\frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 2 = x - \frac{1}{2}
\]

2. **Combine the results**:
\[
\left(\frac{1}{2}x + 2\right) + \left(x - \frac{1}{2}\right)
\]

3. **Combine like terms**:
- **Combine the \(x\) terms**:
\[
\frac{1}{2}x + x = \frac{1}{2}x + \frac{2}{2}x = \frac{3}{2}x
\]
- **Combine the constant terms**:
\[
2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{3}{2}
\]

4. **Final expression**:
Now we have:
\[
\frac{3}{2}x + \frac{3}{2}
\]

5. **Expressing in mixed number form**:
This expression can be factored if necessary, but in mixed number form for the term \( \frac{3}{2} \), you can express it as \( 1 \frac{1}{2} \).
So the entire expression can be written as:
\[
\frac{3}{2}(x + 1)
\]

However, if you wish to give just the constant part in mixed number format, the result is:
\[
\frac{3}{2}x + 1 \frac{1}{2}
\]

If there was any specific part of the question I misunderstood or any specific aspect of the mixed number format you wanted, please let me know!