Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression, we first need to distribute the fractions:

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

Simplifying further, we have:

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

To add the fractions, we need to find a common denominator. The least common multiple of 2 and 4 is 4, so let's convert all the fractions to have a denominator of 4:

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

Now we can simplify the expression:

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

Combining like terms, we have:

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

Next, we add the coefficients together:

(6x + 2)/4

Finally, we simplify the expression, if possible:

The numerator cannot be divided evenly by the denominator, so we write the expression in mixed number form.

(6x + 2)/4 can be written as (6x/4 + 2/4), which simplifies to (3/2x + 1/2).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To add the expression 1/2(x+4) + 1/4(4x-2), we first need to simplify each term.

Step 1: Distribute in both terms:
1/2(x+4) + 1/4(4x-2)
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + 4/4x - 2/4
= 1/2x + 2/2 + x - 1/2

Step 2: Add the like terms together:
1/2x + 2/2 + x - 1/2
= (1/2x + x) + (2/2 - 1/2)
= (1.5x) + (1)
= 1.5x + 1

So, the final answer in mixed number form is 1.5x + 1.

Answer 3

[AI-generated answer — Explain Bot]

To add the given expression, 1/2(x+4)+1/4(4x−2), we need to simplify each term separately and then combine them.

Let's start with simplifying the first term, 1/2(x+4):

To simplify 1/2(x+4), we distribute the 1/2 to both terms inside the parentheses:

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

Next, let's simplify the second term, 1/4(4x−2):

Again, we distribute 1/4 to both terms inside the parentheses:

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

Now, we can combine the simplified terms:

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

To add these terms, we need to have a common denominator, which is 2. So, we convert (x+2)/2 to a fraction with the denominator 2:

(x+2)/2 + 2x/2 - 1/2 = (x+2+2x-1)/2 = (3x+1)/2

Finally, the answer in mixed number form is:

(3x+1)/2

Answer 4

just do the problem

Answer 5

wow like that probably wasn't the FIRST thing they thought of btw the answer is 1 1/2x+1 1/2.