Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To add the given expressions, we need to find a common denominator.

The denominators in the given expressions are 2 and 4. The least common denominator of 2 and 4 is 4.

Now, let's rewrite the given expressions with the common denominator of 4:

1/2(x + 4) = (2/2)(x + 4)/2 = (2x + 8)/4

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

So, the expression becomes:

(2x + 8)/4 + (4x - 2)/4

Now, we can add the numerators and place the sum over the common denominator of 4:

(2x + 8 + 4x - 2)/4

Simplifying the numerator:

(6x + 6)/4

Now, we can write the final answer in mixed number form.

Dividing the numerator by the denominator:

(6x + 6)/4 = 6x/4 + 6/4

Simplifying the fractions:

6x/4 = 3x/2

6/4 = 1+ 2/4 = 1+1/2

So, the final answer in mixed number form is:

3x/2 + 1+1/2

Answer 2

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

To add the given expression, follow these steps:

Step 1: Distribute the 1/2 to the terms inside the parentheses:
1/2(x + 4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1

Step 2: Distribute the 1/4 to the terms inside the parentheses:
1/4(4x - 2) = 1/4 * 4x + 1/4 * (-2) = x - 1/2

Step 3: Add the two simplified expressions together:
(1/2x + 1) + (x - 1/2)

Step 4: Combine like terms:
1/2x + x + 1 - 1/2

Step 5: Combine the x terms:
(1/2x + x) + (1 - 1/2) = (3/2)x + (2/2 - 1/2)

Step 6: Simplify the fractions:
(3/2)x + (1/2) = (3/2)x + 1/2

The final answer in mixed number form is: (3/2)x + 1/2

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem and obtain the answer in mixed number form, we need to simplify the expression step by step. Here's how:

Step 1: Distribute the fractions
Multiply each fraction by the value next to it:
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 + 1x - 1/2

Step 2: Combine like terms
Combine the terms with the same variable (x):
1/2x + 1x + 2/2 - 1/2

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

= 3/2x + 1/2

Step 3: Convert the improper fraction to a mixed number
To convert 3/2 from an improper fraction to a mixed number, divide the numerator (3) by the denominator (2):

3 ÷ 2 = 1 remainder 1

This means that 3/2 can be written as the mixed number 1 1/2.

Therefore, the final answer in mixed number form is:

1 1/2