Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form. pls explain
To subtract 1/2(z+4) - 3(1/4z+1), we first need to distribute the negative sign in front of the 3 to both terms within the parentheses:
1/2(z+4) - [3(1/4z) + 3(1)]
This becomes:
1/2z + 2 - (3/4z + 3)
Now, let's simplify further:
1/2z + 2 - 3/4z - 3
To combine like terms, we need to have a common denominator. In this case, the least common denominator is 4:
(2(2z) + 8 - 3(4z) - 12)/4
Simplifying:
(4z + 8 - 12z - 12)/4
Now, combine the like terms:
(-8z - 4)/4
Finally, simplifying and rewriting in fraction form:
-2z - 1
To subtract the expression 1/2(z+4) - 3(1/4z+1), we need to distribute the 3 to each term inside the parenthesis:
1/2(z+4) - 3(1/4z+1) = 1/2z + 2 - 3/4z - 3
Now, let's combine like terms.
Start with the terms containing z: 1/2z - 3/4z
To subtract fractions, we need to make sure the denominators are the same. The least common denominator (LCD) for 2 and 4 is 4.
Now we rewrite the fractions with the common denominator of 4:
(1/2z) - (3/4z) = (2/4z) - (3/4z) = (2-3)/4z = -1/4z
Next, let's combine the constant terms: 2 - 3 = -1
Finally, the subtracted expression becomes:
-1/4z - 1.
To subtract the fraction expression 1/2(z + 4) - 3(1/4z + 1), we first distribute the coefficients to the terms inside the parentheses. Let's break it down step by step:
Step 1: Distribute the coefficient 1/2 to (z + 4):
(1/2)(z + 4) = (1/2) * z + (1/2) * 4 = 1/2z + 2
Step 2: Distribute the coefficient 3 to (1/4z + 1):
3(1/4z + 1) = 3 * (1/4z) + 3 * 1 = 3/4z + 3
Now that we have simplified the original expression, we can rewrite it as follows:
1/2z + 2 - (3/4z + 3)
Since we want to subtract this expression, we distribute the negative sign to both terms inside the parentheses:
1/2z + 2 - 3/4z - 3
Now, let's combine like terms. The like terms are those with the same variable (z):
1/2z - 3/4z + 2 - 3
To combine the fractions, we need to find a common denominator. In this case, the common denominator is 4:
(2/4z) - (3/4z) + 2 - 3
Now, we can combine the fractions:
(2 - 3)/(4z) + 2 - 3
Simplify further:
(-1)/(4z) - 1
And that's the final answer, with the fractions in their simplest form:
-1/(4z) - 1