https://file.aiquickdraw.com/mathbot/file/17269211890675ni1a9x1.jpg

Let's break down the questions from the image:

### Question 1:
**Determine which statement or statements define a placeholder variable:**
a. The amount of water in my water bottle during the day (assuming it is refilled).
b. The number of people sitting in this classroom at 10:30am today.
c. The World Record time for the men's 200-meter dash.
d. The wait time for seeing an advisor today.

**Answer choices:**
a. B only
b. C only
c. B and C
d. B, C, and D
e. All are Changing Values

**Explanation:**
- A placeholder variable is used to represent a value that can change or is uncertain. Based on this:
  - **a** (water bottle amount): This changes based on how much is consumed/refilled, so it's a changing value.
  - **b** (number of people in the classroom): The number is specific to a moment in time but can vary at different times.
  - **c** (World Record time): The record is a constant value until it changes.
  - **d** (wait time): This can change depending on many factors throughout the day.

So, **B, C, and D** represent changing variables.
**Answer: d. B, C, and D**

---

### Question 2:
**Three less than twice a number is at least 4 more than the number.**

We need to translate the statement into an inequality:
- "Twice a number" is \(2n\).
- "Three less than twice a number" is \(2n - 3\).
- "At least" means greater than or equal to (\(\geq\)).
- "4 more than the number" is \(n + 4\).

Thus, the inequality is:
\[
2n - 3 \geq n + 4
\]

**Answer: d. \(2n - 3 \geq n + 4\)**

---

### Question 3:
**The difference between three times a number and 5.**

We need to translate this into an expression:
- "Three times a number" is \(3n\).
- "Difference between three times a number and 5" means we subtract 5 from \(3n\), giving \(3n - 5\).

**Answer: a. \(3n - 5\)**

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Do you want further clarification or details? Here are 5 related questions for practice:

1. What does it mean for a value to be a constant in math?
2. How would you solve the inequality \(2n - 3 \geq n + 4\)?
3. What is the solution set for \(3n - 5 = 10\)?
4. How do you interpret "4 less than a number" in algebra?
5. What is the difference between an equation and an inequality?

**Tip:** When translating word problems into equations or inequalities, always break the sentence down into smaller parts and match them with mathematical operations.

MAT055 Final Exam: Placeholder variables, inequalities, and algebraic expressions

This final exam covers important mathematical concepts such as identifying placeholder variables, solving inequalities, and translating word problems into algebraic expressions. Questions include recognizing changing variables, forming inequalities, and writing expressions like 3n - 5.

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