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

Answer 1

To simplify the expression, we combine like terms.

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

Using the distributive property, we distribute the fractions.

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

Simplifying further:

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

Combining like terms:

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

Now, we can combine the fractions:

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

To add fractions with different denominators, we need to find a common denominator. In this case, the least common denominator is 2. Therefore, we need to rewrite the fractions:

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

Simplifying:

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

Now, we add the fractions with the same denominator:

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

Simplifying the fractions:

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

Adding the fractions and simplifying further:

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

Now, we combine the fractions:

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

To add the fractions, we need a common denominator. The least common denominator is 2x. Therefore, we rewrite the fractions:

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

Expanding the denominators:

3x/2x + x/2x

Now, we combine the fractions:

(3x + x)/2x

Simplifying further:

4x/2x

Dividing the numbers:

4/2

Simplifying:

2

Therefore, the answer in mixed number form is 2.

Answer 2

can you make the answer more clear??

Answer 3

Apologies for any confusion. To simplify the expression 1/2(x + 4) + 1/4(4x - 2) and express the answer in mixed number form:

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

Using the distributive property, we distribute the fractions:

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

Simplifying further:

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

Combining like terms:

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

Simplifying the fractions:

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

Now, we rearrange the terms, grouping similar terms:

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

Combining the fractions with the same denominator:

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

Simplifying the fractions:

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

Adding the fractions and simplifying further:

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

Combining the fractions:

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

To add the fractions, we need a common denominator. The least common denominator is 2x. Therefore, we rewrite the fractions:

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

Expanding the denominators:

(3x/2x) + (x/2x)

Now, we combine the fractions:

(3x + x)/2x

Simplifying further:

4x/2x

Dividing the numbers:

4/2

Simplifying:

2

Therefore, the answer to the expression 1/2(x + 4) + 1/4(4x - 2) in mixed number form is 2.

Answer 4

are there answers other than 2?

Answer 5

Apologies for the confusion. Let's reevaluate the expression to ensure we haven't missed any possible answers.

To simplify the expression: 1/2(x + 4) + 1/4(4x - 2)

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

Using the distributive property, we distribute the fractions:

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

Simplifying further:

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

Combining like terms:

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

Simplifying the fractions:

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

Now, we rearrange the terms, grouping similar terms:

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

Combining the fractions with the same denominator:

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

Simplifying the fractions:

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

Adding the fractions and simplifying further:

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

Combining the fractions:

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

To add the fractions, we need a common denominator. The least common denominator is 2x. Therefore, we rewrite the fractions:

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

Expanding the denominators:

(3x/2x) + (x/2x)

Now, we combine the fractions:

(3x + x)/2x

Simplifying further:

4x/2x

Dividing the numbers:

4/2

Simplifying:

2

After reevaluating the expression, the only possible answer is 2.