Subtract 1/2 (z + 4) – 3( 1/4 z+1). Use fractions in final form.

Question

Answer: - 1/4 z - 1
Describe as a 7th grader in short and simple sentences + show all your work.

Answer 1

Let's solve the problem step by step.

We need to subtract \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \).

Step 1: Distribute \( \frac{1}{2} \) to \( (z + 4) \)

When we multiply, we do: \[ \frac{1}{2} \times z + \frac{1}{2} \times 4 = \frac{1}{2}z + 2 \] So, \( \frac{1}{2}(z + 4) = \frac{1}{2}z + 2 \).

Step 2: Distribute \( -3 \) to \( \left( \frac{1}{4} z + 1 \right) \)

First, multiply: \[ -3 \times \frac{1}{4}z + (-3) \times 1 = -\frac{3}{4}z - 3 \] So, \( -3\left(\frac{1}{4}z + 1\right) = -\frac{3}{4}z - 3 \).

Step 3: Write the whole expression together

Now, we look at the original problem again: \[ \frac{1}{2}z + 2 - \left(\frac{3}{4}z + 3\right) \] This becomes: \[ \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \]

Step 4: Combine like terms

First, let's combine the \( z \) terms. We have: \[ \frac{1}{2}z - \frac{3}{4}z \] To do this, we need to have a common denominator. The common denominator for 2 and 4 is 4.

So we change \( \frac{1}{2}z \) to \( \frac{2}{4}z \): \[ \frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z \]

Now we combine the constant terms: \[ 2 - 3 = -1 \]

Step 5: Put it all together

So our final answer is: \[ -\frac{1}{4}z - 1 \]

In short, we found that when you subtract \( \frac{1}{2}(z + 4) \) and \( 3\left(\frac{1}{4}z + 1\right) \), you get: \[ -\frac{1}{4}z - 1 \]

Answer 2

can you shorten it more and change it all into text form

Answer 3

Sure! Here’s a shorter text version:

To solve \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \):

1. Distribute \( \frac{1}{2} \) to \( (z + 4) \):

   • \( \frac{1}{2} \times z + \frac{1}{2} \times 4 = \frac{1}{2}z + 2 \)

2. Distribute \( -3 \) to \( \left( \frac{1}{4}z + 1 \right) \):

   • \( -3 \times \frac{1}{4}z + -3 \times 1 = -\frac{3}{4}z - 3 \)

3. Combine the results:

   • We have \( \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \).

4. Combine like terms:

   • For the \( z \) terms: \( \frac{1}{2}z - \frac{3}{4}z = -\frac{1}{4}z \) (after finding a common denominator).
   • For the constants: \( 2 - 3 = -1 \).

Final answer: \( -\frac{1}{4}z - 1 \).

Answer 4

can you shorten it some more

Answer 5

Certainly! Here’s the very short version:

To solve \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \):

1. Distribute:

   • \( \frac{1}{2}(z + 4) = \frac{1}{2}z + 2 \)
   • \( -3\left(\frac{1}{4}z + 1\right) = -\frac{3}{4}z - 3 \)

2. Combine:

   • \( \frac{1}{2}z - \frac{3}{4}z + 2 - 3 = -\frac{1}{4}z - 1 \)

Final answer: \( -\frac{1}{4}z - 1 \).

Answer 6

can you change it all into text form and thank you

Answer 7

Of course! Here’s everything in text form:

To solve the expression \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \), follow these steps:

First, distribute \( \frac{1}{2} \) to the terms inside the parentheses. This gives you \( \frac{1}{2}z + 2 \).

Next, distribute \( -3 \) to the terms inside the second parentheses. This results in \( -\frac{3}{4}z - 3 \).

Now, combine these results to create the full expression: \( \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \).

Combine the like terms. For the \( z \) terms, \( \frac{1}{2}z - \frac{3}{4}z \) simplifies to \( -\frac{1}{4}z \). For the constant terms, \( 2 - 3 \) equals \( -1 \).

Putting it all together, the final answer is \( -\frac{1}{4}z - 1 \).

Thank you! If you have any more questions, feel free to ask!

Answer 8

the fractions are images can you put them in text instead

Answer 9

Absolutely! Here’s the solution using text for the fractions:

To solve the expression (1/2)(z + 4) - 3(1/4z + 1), follow these steps:

First, distribute 1/2 to the terms inside the parentheses. This gives you (1/2)z + 2.

Next, distribute -3 to the terms inside the second parentheses. This results in -(3/4)z - 3.

Now, combine these results to create the full expression: (1/2)z + 2 - (3/4)z - 3.

Combine the like terms. For the z terms, (1/2)z - (3/4)z simplifies to -(1/4)z. For the constant terms, 2 - 3 equals -1.

Putting it all together, the final answer is -(1/4)z - 1.

Thank you! If you have any more questions, feel free to ask!