Question

Subtract 1/2 (z + 4) - 3 (1/4z +1). Use fractions in final form.

Answer 1

use fractions in final form

Answer 2

To solve this problem, we can distribute and simplify each term:

First, let's distribute and simplify the first term:
1/2 * z + 1/2 * 4 = 1/2 * z + 2 = z/2 + 2

Next, let's distribute and simplify the second term:
3 * 1/4z + 3 * 1 = 3/4z + 3

Now, let's subtract the two terms:
(z/2 + 2) - (3/4z + 3)

Next, let's find a common denominator for the fractions in the equation. The common denominator for 2 and 4 is 4. Multiply every term by 4 to get rid of the denominators:

(4 * z/2 + 4 * 2) - (4 * 3/4z + 4 * 3)

This simplifies to:
(2z + 8) - (3z + 12)

Now, let's expand the equation:
2z + 8 - 3z - 12

Combining like terms:
(2z - 3z) + (8 - 12) = -z - 4

Therefore, the final answer is -z - 4.

Answer 3

Sure, to write the final answer in fraction form, we can use the least common denominator approach. The least common denominator for the fractions involved is 4z.

Subtracting the fractions:

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

To find a common denominator, multiply the numerator and denominator of the first fraction by 2 and the numerator and denominator of the second fraction by 4:

(2/4)z - (12/4)z + 4

Now, we can combine the fractions:

(2z - 12z) / 4z + 4

Simplifying the numerator:

(-10z) / 4z + 4

Now, let's simplify the denominator:

4z + 4

Therefore, the final answer is (-10z) / (4z + 4).