add 1/2 (x + 4) + 1/4 (4x - 2) in mixed form

Answer 1

To add the expression 1/2 (x + 4) + 1/4 (4x - 2) in mixed form, we first simplify each expression separately, and then combine like terms.

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, we can combine the simplified expressions:

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

To add these terms with unlike denominators, we need to find a common denominator. The least common multiple (LCM) of 2 and 1 is 2. Thus, we need to adjust the fractions to have a denominator of 2:

1/2x + 2 + x - 1/2 = 1/2x + x + 4/2 - 1/2 = 3/2x + 4/2 + 1/2 - 1/2

Now we can combine the numerators:

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

Simplifying the numerator:

= (3x + 4)/2

Therefore, the expression 1/2 (x + 4) + 1/4 (4x - 2) in mixed form is (3x + 4)/2.

Answer 2

can you add this???

Answer 3

My apologies for the error in my previous response. Let's add the expression 1/2 (x + 4) + 1/4 (4x - 2) correctly.

First, distribute the fractions:

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

Next, combine like terms:

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

To add 2 and -1/2, we need a common denominator, which is 2:

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

In mixed form, we can write this as:

= 1 and 1/2x

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