Add: 1/2 ( x + 4 ) + 1/4 ( 4 x − 2 )

Question

. Answer should be in mixed number form.(1 point)

Answer 1

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: $$(\frac{1}{2}x+2)+(x-\frac{1}{2})$$

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 2

no

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: $$(\frac{1}{2}x+2)+(x-\frac{1}{2})$$

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!