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

Answer 1

To simplify the expression, let's simplify each term separately:

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

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

Now let's add the two simplified terms:

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

The denominators of 2 and 1/2 are different, so we need to find a common denominator. The least common multiple of 2 and 1/2 is 2.

So, we multiply each term by 2 to get a common denominator:

(3/2x)⋅2 + 2⋅2 - (1/2)⋅2

= 3x + 4 - 1

= 3x + 3

Therefore, 1/2( x + 4) + 1/4 (4x - 2) simplified to mixed number form is 3x + 3.

Answer 2

It said it was incorrect..

Answer 3

I apologize for the confusion. Let's try again:

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

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

Now let's add the two simplified terms:

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

Combine like terms:

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

To convert this to mixed number form, we divide the numerator (3) by the denominator (2):

3 divided by 2 is 1 with a remainder of 1

So, we have 1 and 1/2.

Therefore, 1/2( x + 4) + 1/4 (4x - 2) simplified to mixed number form is 1 1/2.

Answer 4

Still said incorrect ;(

Answer 5

I apologize for the confusion. Let's try solving it again:

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

Distribute the fractions:

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

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

Simplify the fractions:

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

Combine like terms:

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

3/2x + 1/2

Now, let's convert this to mixed number form:

The whole number part is obtained by dividing the numerator (3) by the denominator (2):

3 divided by 2 is 1 with a remainder of 1

So, the whole number part is 1.

The fractional part is 1/2.

Therefore, the final answer is 1 1/2.

Answer 6

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

Answer 7

Apologies for the confusion. Let's solve it again:

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

Distribute the fractions:

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

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

Simplify the fractions:

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

Combine like terms:

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

Adding the coefficients of x:

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

3/2 x + 1 - 1/2

Now, to convert it to a mixed number, let's find a common denominator for 2 and 1/2, which is 2.

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

3x/2 - 1/2

Now, let's simplify:

3x - 1/2

As a mixed number, it can be written as:

2 1/2x - 1/2

Therefore, the answer in mixed number form is 2 1/2x - 1/2.

Answer 8

Wrong

Answer 9

Apologies for the mistake. Let's solve it again:

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

Distribute the fractions:

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

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

Simplify the fractions:

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

Combine like terms:

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

3/2x + 1/2

Now, let's convert it to a mixed number:

The whole number part is obtained by dividing the numerator (3) by the denominator (2):

3 divided by 2 is 1 with a remainder of 1

So, the whole number part is 1.

The fractional part is 1/2.

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