Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form pls show work

Answer 1

To subtract 1/2(z+4) - 3(1/4z+1), we need to first distribute the coefficients to each term inside the parentheses.

Starting with the first term, we distribute 1/2 to (z+4):

1/2 * z = z/2
1/2 * 4 = 4/2 = 2

So, the first term becomes: z/2 + 2

Now, let's distribute 3 to (1/4z+1):

3 * 1/4z = 3/4z
3 * 1 = 3

So, the second term becomes: 3/4z + 3

Now we can simplify the expression:

(z/2 + 2) - (3/4z + 3)

Notice that we have a common denominator of 2 for the first term and a common denominator of 4 for the second term. To combine the terms, we need a common denominator. Let's find the least common multiple:

The least common multiple of 2 and 4 is 4.

To convert the first term to have a denominator of 4, we multiply both the numerator and denominator by 2:

(z/2 + 2) = (2z/4 + 4)

Now, the expression becomes:

(2z/4 + 4) - (3/4z + 3)

We can now combine the like terms:

2z/4 - 3/4z + 4 - 3

Next, let's combine the z terms and the constant terms separately:

For the z terms: 2z/4 - 3/4z
To subtract, we need to find a common denominator of 4:
(2z - 3)/4z

For the constant terms: 4 - 3 = 1

So, the final simplified expression is:

(2z - 3)/4z + 1