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

Answer 1

To add 1/2(x+4) + 1/4(4z-2) in mixed form, first distribute the fractions:

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

Simplifying the distributed fractions:

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

Now, we combine like terms:

1/2*x + 2 + z - 1/2

Next, simplify the fractions:

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

Now, let's find a common denominator to combine the fractions:

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

Combining like terms:

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

Simplifying the fractions:

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

Combining the whole numbers and fractions:

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

So, 1/2(x+4) + 1/4(4z-2) in mixed form is (x/2 + 3/2) + 2z.