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

Answer 1

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