Question

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

Answer 1

To subtract the expression 1/2 (z + 4) - 3 (1/4z + 1), distribute the fractions, combine like terms, and ensure common denominators to simplify to -1/4z - 1.

Step-by-step explanation:

Step-by-step Solution

To solve the expression 1/2 (z + 4) - 3 ( 1/4z + 1), first distribute the fractions across the terms inside the parentheses:

Multiply ½ by both z and 4 to get ½z + 2.

Multiply 3 by both ¼z and 1 to get ¾z + 3.

The expression now reads ½z + 2 - (¾z + 3).

Distribute the negative sign to both terms in the second expression: ½z + 2 - ¾z - 3.

Combine like terms to simplify: (½ - ¾)z and (2 - 3), which gives us -¼z - 1.

To find a common denominator for ½ and ¾, we must understand that the least common multiple of their denominators is 4. By converting ½ to 2/4, we're able to subtract it from ¾ and proceed with the calculation.

This gives us a final answer of -¼z - 1 in fraction form.

Answer 2

The subtraction of 1/2 (z + 4) - 3 (1/4z + 1) simplifies to (-1/4)z - 1 by first distributing the fractions, then combining like terms.

Step-by-step explanation:

To subtract 1/2 (z + 4) - 3 (1/4z + 1), we first need to distribute the fractions across the terms inside the brackets:

• For the first expression 1/2 (z + 4), this becomes (1/2)z + (1/2)*4, which simplifies to (1/2)z + 2.
• For the second expression 3 (1/4z + 1), distributing would give us 3*(1/4)z + 3*1, which simplifies to (3/4)z + 3.

Next we combine the like terms:

• The z terms: (1/2)z - (3/4)z simplifies to (-1/4)z after finding a common denominator and subtracting.
• The constant terms: 2 - 3 equals -1.

Therefore, the final expression after subtraction is (-1/4)z - 1.