https://file.aiquickdraw.com/mathbot/file/1726205317910ujuwunfi.jpg

Let's go through the questions based on the image:

### Question 3
**If \( p \) represents an unknown number of six-packs of beer, state what each of the expressions represents:**
- **(a) \( 3p \)**: This represents three times the number of six-packs of beer. If \( p \) is the number of six-packs, then \( 3p \) represents the total number of beers in three six-packs, which would be \( 3 \times p \times 6 \), or \( 18p \) individual beers.
- **(b) \( p + 1 \)**: This represents one more than the number of six-packs. If \( p \) is the number of six-packs, then \( p + 1 \) represents having one additional six-pack.

### Question 4
**Build the expression step by step (DO NOT SIMPLIFY):**
- The difference between 4 and 7: \( 4 - 7 \)
- The quantity is raised to the 3rd power: \( (4 - 7)^3 \)
- The new quantity is added by 2: \( (4 - 7)^3 + 2 \)
- The sum is divided by 5: \( \frac{(4 - 7)^3 + 2}{5} \)
- The quotient is multiplied by -1: \( -\frac{(4 - 7)^3 + 2}{5} \)

Thus, the final expression is: 
\[
-\frac{(4 - 7)^3 + 2}{5}
\]

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Would you like more details or clarifications on these steps?

Here are some follow-up questions:
1. How does the expression \( 3p \) change if you have different values of \( p \)?
2. What does \( p + 1 \) represent in a practical situation involving six-packs?
3. How does raising a negative number to the third power affect its sign?
4. What are the steps to simplify the final expression in question 4?
5. Why is the quotient multiplied by -1 in the final step?

**Tip:** When dealing with algebraic expressions, always follow the order of operations (PEMDAS) to avoid errors.

If p represents an unknown number of six-packs of beer, state what each of the expressions represents:

(a) 3p
(b) p + 1

State each alteration on a separate line to build the following expression (DO NOT SIMPLIFY):

- The difference between 4 and 7
- The quantity is raised to the 3rd power
- The new quantity is added by 2
- The sum is divided by 5
- The quotient is multiplied by -1

Learn how to work with algebraic expressions that involve multiplication, addition, and exponents. This problem also covers operations with numbers and the correct order of steps, following PEMDAS, including raising to the 3rd power, dividing, and multiplying by negative numbers. Suitable for Grades 6-8.

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