Question

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

Answer 1

To subtract, we need to distribute the numbers outside the parentheses to every term inside the parentheses:

1/2(z + 4) distributes to 1/2 * z + 1/2 * 4, which simplifies to 1/2z + 2.
The other term, 3(1/4z + 1), distributes to 3 * 1/4z + 3 * 1, which simplifies to 3/4z + 3.

Next, we subtract the two terms:
1/2z + 2 - (3/4z + 3).

To subtract fractions, we need to get a common denominator. The least common denominator (LCD) between 2 and 4 is 4.

To make 2 have a denominator of 4, we multiply the numerator and denominator by 2:
2 * 2 / 2 = 4 / 2 = 2.

To make 3 have a denominator of 4, we multiply the numerator and denominator by 4:
3 * 4 / 4 = 12 / 4 = 3.

Now, we can rewrite the expression with a common denominator:
1/2z + 2 - (3/4z + 3) = 1/2z + 2 - 3/4z - 3.

We can then reorder the expression to group like terms together:
(1/2z - 3/4z) + (2 - 3).

To subtract fractions with the same denominator, we subtract the numerators while keeping the denominator the same:
1/2z - 3/4z = (2/4 - 3/4)z = (-1/4)z.

So the expression becomes:
(-1/4)z + (2 - 3).

We can simplify this further by combining like terms:
(-1/4)z + (2 - 3) = (-1/4)z - 1.

Therefore, the final answer is (-1/4)z - 1.