Question

Subtract 1/2(z+4)−3(1/4z+1) use fractions in final form.

Answer 1

To subtract 1/2(z+4)−3(1/4z+1), distribute the fractions, find a common denominator, and combine like terms, resulting in the final simplified form of -1/4z - 1.

Step-by-step explanation:

To subtract 1/2(z+4)−3(1/4z+1) we first distribute the fractions within each term and simplify:

• 
  1/2(z+4) becomes 1/2z + 1/2*4 which is 1/2z + 2.
  
• 
  3(1/4z+1) becomes 3*1/4z + 3*1 which is 3/4z + 3.
  

Now, we combine like terms:

1. 
   Subtract 3/4z from 1/2z. To find a common denominator, note that 2 and 4 are both factors of 4. So convert 1/2z to 2/4z. Now subtract: 2/4z - 3/4z = -1/4z.
   
2. 
   Subtract 3 from 2: 2 - 3 = -1.
   

Our final answer is -1/4z - 1.

This process involves using what we know about adding and subtracting fractions with the common denominator scheme, intuitive understanding, and math operations to successfully simplify the expression.