Question

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

Answer 1

That's wrong

Answer 2

To solve this equation, we need to simplify and combine like terms.

First, let's simplify 1/2(x+4):
1/2(x+4) = 1/2*x + 1/2*4 = 1/2*x + 2

Now, let's simplify 1/4(4x-2):
1/4(4x-2) = 1/4*4x - 1/4*2 = x - 1/2

Now we can combine the two simplified expressions:

1/2(x+4) + 1/4(4x-2) = 1/2*x + 2 + x - 1/2

Next, let's combine like terms:

1/2*x + 1/2*x + 2 - 1/2 = x + 1/4

Now, let's write the final answer in mixed number form. Assuming x is a whole number:

x + 1/4 = x + 0.25

Therefore, the answer in mixed number form is x + 0.25.

Answer 3

Apologies for the previous inaccurate response. Let's try solving the equation correctly.

1/2(x+4) + 1/4(4x-2)

To simplify, we first distribute the fractions to their respective terms:

1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2

Simplifying each term gives us:

x/2 + 2/2 + 4x/4 - 2/4

Combining the like terms with the same denominator:

x/2 + 2/2 + (4x - 2)/4

We can simplify 2/2 to 1:

x/2 + 1 + (4x - 2)/4

We need to find a common denominator for the fractions, which is 4. We rewrite the first term with a denominator of 4:

2x/4 + 1 + (4x - 2)/4

Combining the numerators:

(2x + 4 + 4x - 2)/4

Simplifying further:

(6x + 2)/4

To express this as a mixed number, we divide the numerator by the denominator:

6x/4 + 2/4
= 3x/2 + 1/2

Therefore, the final answer in mixed number form is 3x/2 + 1/2.