Subtract 1/2(x+4) - 3 (1/4z+1)

To subtract the expression 1/2(x+4) - 3(1/4z+1), we can distribute the coefficients and then combine like terms.

First, distribute the coefficients:
1/2(x+4) becomes 1/2 * x + 1/2 * 4 = 1/2x + 2

3(1/4z+1) becomes 3 * 1/4z + 3 * 1 = 3/4z + 3

Now, we can subtract the two expressions:
1/2x + 2 - (3/4z + 3)

To simplify the expression further, we need to have the same denominator for both terms. The least common denominator (LCD) for 2 and 4 is 4, so we can rewrite 2 as 2 * 2/2 = 4/2.

In this case, we can multiply the first term by 2/2 and the second term by 4/4, which gives us:
(1/2)x * 2/2 + 4/2 - (3/4)z * 4/4 - 3 * 4/4

Simplifying this, we get:
(2/4)x + 4/2 - (12/4)z - 12/4

Combining like terms, we have:
(2/4)x - (12/4)z + (4/2) - (12/4)

The terms (2/4)x and (12/4)z have the same denominator so we can combine them:
(2x - 12z)/4 + (4/2) - (12/4)

Further simplifying:
(2x - 12z)/4 + 2 - 3

To add 2 and -3, we can rewrite -3 as -3/1 to have the same denominator as 4, and then combine:
(2x - 12z)/4 + 2 - 3/1 = (2x - 12z)/4 + 2 - 3/4 = (2x - 12z - 3)/4

Therefore, the final result of subtracting 1/2(x+4) - 3(1/4z+1) is (2x - 12z - 3)/4.

Use fractions in final form

Apologies for the confusion. Let's rewrite the expression using fractions in the final form.

The expression 1/2(x+4) - 3(1/4z+1) can be rewritten as:

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

To perform the subtraction, we need to have a common denominator for the fractions involved. The least common denominator (LCD) for 2 and 4 is 4. So, we can rewrite 2 as 4/2:

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

Next, let's combine like terms:

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

Now, let's combine the first two terms and the last two terms:

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

Therefore, the final result of subtracting 1/2(x+4) - 3(1/4z+1) is (1/2) x - (3/4) z - 1.