Question

Add: 1/2(x+4)+1/4(4x−2) .

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 1/2(x + 4) + 1/4(4x - 2), we'll first distribute the 1/2 and 1/4 across the parentheses.

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

Simplifying further,

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

= 1/2x + 1 + x - 1/2

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

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

So, the simplified form of 1/2(x + 4) + 1/4(4x - 2) is (3/2x) + (1/2).

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake.

To simplify the expression 1/2(x + 4) + 1/4(4x - 2), we'll first distribute the fractions across the parentheses.

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

Simplifying further,

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

= 1/2x + 1 + x - 1/2

Combine like terms,

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

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

So, the simplified form of 1/2(x + 4) + 1/4(4x - 2) is (3/2x) + (1/2).

Answer 4

still wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the persistent errors. Let's try solving the expression correctly:

To simplify 1/2(x + 4) + 1/4(4x - 2), we'll begin by distributing the fractions across the parentheses:

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

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

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

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

Next, we'll simplify each fractional coefficient:

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

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

Combining like terms:

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

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

= (3/2)x + 1/2

Therefore, the simplified form of 1/2(x + 4) + 1/4(4x - 2) is (3/2)x + 1/2.

Answer 6

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

To add the given expression, 1/2(x+4) + 1/4(4x−2), you need to simplify it by combining like terms.

First, let's simplify each term separately:

1/2(x+4) can be expanded by multiplying 1/2 by both x and 4:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2

1/4(4x−2) can be expanded similarly:
1/4(4x−2) = 1/4 * 4x + 1/4 * (-2) = x - 1/2

Now we can add the two simplified terms together:
1/2x + 2 + x - 1/2

Next, we need to find a common denominator for the fractions. The least common denominator between 2 and 1/2 is 2. So let's rewrite the expression with the common denominator:

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

Finally, combine like terms:
1/2x + 2x + 4 - 1 = 2 1/2x + 3

Therefore, the simplified expression is 2 1/2x + 3.

Answer 7

[AI-generated answer — Explain Bot]

To add the given expression 1/2(x+4) + 1/4(4x−2), we need to simplify it step by step.

Let's start by simplifying the terms within the parentheses:

1/2(x+4) becomes (1/2)x + (1/2) * 4, which simplifies to (1/2)x + 2

1/4(4x−2) can be written as (1/4) * 4x - (1/4) * 2, which simplifies to x - (1/2)

Now we can add these simplified expressions together:

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

Next, we combine like terms. The x terms combine to give us (1/2)x + x = (3/2)x. The constant terms, 2 and - (1/2), combine to give us 2 - (1/2) = 3/2.

So, the final simplified expression is:

(3/2)x + 3/2