Subtract 1/2(z + 4) - 3 (1/4z + 1). Use fractions in final form
To subtract the fractions, we need to first distribute the fractions in each term before subtracting.
Firstly, let's distribute 1/2 across (z+4):
1/2(z + 4) = 1/2 * z + 1/2 * 4 = 1/2z + 2
Next, let's distribute -3 across (1/4z + 1):
-3(1/4z + 1) = -3 * 1/4z + (-3) * 1 = -3/4z - 3
Now, let's subtract the two terms:
1/2z + 2 - 3/4z - 3 = (1/2z - 3/4z) + (2 - 3)
To combine the fractions with the same denominator, we'll need to find a common denominator. In this case, the common denominator is 4:
1/2z - 3/4z = 2/4z - 3/4z = (2-3)/4z = -1/4z
So, the final form after the subtraction is -1/4z + (2 - 3) = -1/4z - 1. Answer: -1/4z - 1.
To simplify the expression, we need to distribute and combine like terms.
Let's do it step-by-step:
Step 1: Distribute the first term (1/2) to both terms inside the parentheses.
(1/2) * (z) + (1/2) * (4) - 3(1/4z) - 3(1)
Simplify this:
1/2(z) = (1/2)z
1/2(4) = (1/2) * (4) = 2
So, the expression becomes:
(1/2)z + 2 - 3(1/4z) - 3(1)
Step 2: Distribute the second term (-3) to both terms inside the parentheses.
(1/2)z + 2 - (3/4z) - 3
Simplify this:
-3(1) = -3
So, the expression becomes:
(1/2)z + 2 - (3/4z) - 3
Step 3: Combine like terms.
The expression becomes:
(1/2)z - (3/4)z + 2 - 3
Combine the z terms:
(1/2 - 3/4)z + 2 - 3
To combine the fractions, we need to find a common denominator, which is 4.
(2/4 - 3/4)z + 2 - 3
Simplify this:
(-1/4)z + 2 - 3 = (-1/4)z - 1
So, the simplified expression is:
(-1/4)z - 1
To subtract 1/2(z + 4) - 3 (1/4z + 1) using fractions, we need to simplify each term and then combine like terms. Let's start by simplifying each expression:
1/2(z + 4) = (1/2)z + (1/2) * 4 = 1/2z + 2
1/4z + 1 = (1/4)z + 1 = 1/4z + 4/4 = 1/4z + 4/4 = 1/4z + 1
Now, we can substitute these simplified expressions back into the original equation:
1/2z + 2 - 3(1/4z + 1)
Next, we can distribute the -3 to every term inside the parentheses:
1/2z + 2 - 3/4z - 3
To combine like terms, we group the z terms together and the constant terms together:
(1/2z - 3/4z) + (2 - 3)
To combine the z terms, we need to find a common denominator. The least common multiple (LCM) of 2 and 4 is 4, so we can multiply the numerator and denominator of (1/2z) by 2:
(2/4z - 3/4z) + (2 - 3)
Simplifying further:
(-1/4z) + (-1)
Finally, combining the like terms in parentheses:
-1/4z - 1
Therefore, the final result after subtracting is -1/4z - 1.