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

Question

help please

Answer 1

To add the given expressions, first simplify each fraction separately:

1/2(x + 4) can be rewritten as (x + 4) / 2.

1/4(4x - 2) can be rewritten as (4x - 2) / 4.

Now, combine the fractions by finding a common denominator, which in this case is 4.

Multiply the numerator and denominator of (x + 4) / 2 by 2 to get (2(x + 4)) / (2 * 2) = (2x + 8) / 4.

Now add (2x + 8) / 4 and (4x - 2) / 4:

(2x + 8 + 4x - 2) / 4 = (6x + 6) / 4.

Finally, simplify the resulting fraction:

(6x + 6) / 4 can be rewritten in mixed number form as 6(x + 1) / 4 = 6/4(x + 1) = 3/2(x + 1).

So, the answer in mixed number form is 3/2(x + 1).

Answer 2

its wrong

Answer 3

I apologize for the previous incorrect response. Let's try solving the expression correctly:

1/2(x + 4) can be expanded to (1/2 * x) + (1/2 * 4) = (1/2)x + 2.

1/4(4x - 2) can be expanded to (1/4 * 4x) - (1/4 * 2) = x - 1/2.

Now, let's add both terms:

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

To add the terms, we need to find a common denominator. The common denominator of 2 and 4 is 4.

Multiplying the first term by 2/2 and the second term by 4/4:

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

Simplifying:

(6/4)x + (2/4) - (2/4)

Now, let's combine like terms:

(6/4)x + (2/4) - (2/4) = (6/4)x = (3/2)x

So, the final answer in mixed number form is 3/2x.

Answer 4

your also wrong its supposed to be in MIXED NUMBER FORM

Answer 5

Apologies for the confusion. Let's express the answer in mixed number form.

To start, let's simplify the given expression:

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

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

Now, let's add the fractions:

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

To add these fractions, we need a common denominator. The least common multiple of 2 and 4 is 4.

Multiplying the first fraction by 2/2 and the second fraction by 1/1:

[(x + 4) * 2] / (2 * 2) + [(4x - 2) * 1] / (1 * 4)
(2x + 8) / 4 + (4x - 2) / 4

Now, let's combine the numerators:

(2x + 8 + 4x - 2) / 4 = (6x + 6) / 4

To express this fraction in mixed number form, we divide the numerator by the denominator:

(6x + 6) ÷ 4

Dividing 6x by 4 gives us 1.5x, and dividing 6 by 4 gives us 1. Therefore, the expression can be written as:

1 1/2x

Answer 6

nvm thanks for not helping and giving wrong answers

Answer 7

I apologize for the incorrect responses earlier. Let's attempt to solve the expression correctly and provide the answer in mixed number form.

Starting with the expression: 1/2(x + 4) + 1/4(4x - 2)

We can distribute and simplify each term as follows:

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

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

Now, let's add the two terms:

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

To add the fractions, we find a common denominator, which is 2:

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

This simplifies to:

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

Combining like terms:

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

Simplifying further:

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

Combining similar fractions:

(2/4x + 4/4x) + (4/4 - 1/4) = (6/4x) + (3/4)

Now, divide the numerator by the denominator:

(6/4x) + (3/4) = 3/2x + 3/4

In mixed number form, this can be written as:

1 3/2x + 3/4

Therefore, the answer in mixed number form is 1 3/2x + 3/4.