Subtract 1/2(z + 4) - 3(1/4z + 1). Use fractions in final form.
To subtract 1/2(z + 4) - 3(1/4z + 1), let's simplify each term step by step:
1/2(z + 4) = 1/2 * z + 1/2 * 4 = 1/2z + 2
3(1/4z + 1) = 3 * 1/4z + 3 * 1 = 3/4z + 3
Now, we can subtract the two simplified terms:
1/2z + 2 - (3/4z + 3)
To subtract fractions, we need to have a common denominator. In this case, the common denominator is (2 * 4 = 8):
(4/8z + 16/8) - (6/8z + 24/8)
Now, we can combine like terms:
(4z + 16) / 8 - (6z + 24) / 8
= (4z - 6z + 16 - 24) / 8
= (-2z - 8) / 8
= -2z/8 - 8/8
= -z/4 - 1
Therefore, the final simplified form of 1/2(z + 4) - 3(1/4z + 1) is -z/4 - 1.
To subtract 1/2(z + 4) - 3(1/4z + 1), we can distribute the coefficients to the terms inside the parentheses.
First, distribute 1/2 to (z + 4):
1/2 * z = 1/2z
1/2 * 4 = 2
So, 1/2(z + 4) becomes 1/2z + 2.
Next, distribute 3 to (1/4z + 1):
3 * 1/4z = 3/4z
3 * 1 = 3
So, 3(1/4z + 1) becomes 3/4z + 3.
Now, we can subtract the two terms: (1/2z + 2) - (3/4z + 3).
To subtract fractions, we need a common denominator. The least common denominator (LCD) for 2 and 4 is 4, so we can rewrite 2 as 8/4.
Now, we have (1/2z + 8/4) - (3/4z + 3).
To subtract fractions, we combine the numerators over the common denominator, which is 4:
(1/2z + 8/4) - (3/4z + 3) = (1/2z + 2z/4) - (3/4z + 3)
Next, we can simplify the fractions by finding a common denominator of 4:
(1/2z + 2z/4) - (3/4z + 3) = (2/4z + 2z/4) - (3/4z + 3)
Now, we can combine the numerators over the common denominator:
(2/4z + 2z/4) - (3/4z + 3) = (2 + 2z)/4z - (3 + 12z)/4z
To subtract fractions with the same denominator, we subtract the numerators:
(2 + 2z)/4z - (3 + 12z)/4z = (2 + 2z - 3 - 12z)/4z
Combining like terms:
(2 + 2z - 3 - 12z)/4z = (-10z - 1)/4z
So, the final result is (-10z - 1)/4z.
To find the result of the expression, we need to simplify and combine like terms. Let's start by distributing the numbers outside the parentheses to each term inside.
1/2 * (z + 4) = 1/2 * z + 1/2 * 4 = 1/2 * z + 2
3 * (1/4 * z + 1) = 3 * 1/4 * z + 3 * 1 = 3/4 * z + 3
Now we can rewrite the given expression as:
1/2 * z + 2 - (3/4 * z + 3)
Next, we need to subtract the two terms inside the parentheses. To do this, let's distribute a negative sign to all terms within the second parentheses.
1/2 * z + 2 - 3/4 * z - 3
Now, we can combine like terms. We have two terms with z and two constant terms.
(1/2 * z - 3/4 * z) + (2 - 3)
To simplify the algebraic expression, we can find a common denominator for the fractions.
The common denominator for 2 and 3 is 4.
Multiplying both terms with z by 4/4, we get:
(2/4 * z - 3/4 * z) + (2 - 3)
Simplifying further, we have:
(-1/4 * z) + (-1)
The final result is:
-1/4 * z - 1