Week 4 Final Assignment Inequalities and the Coordinate Plane

✅ Week 4 Assignment: Linear Inequalities & Polynomials

Textbook: OpenStax Intermediate Algebra
Chapters Covered:

  • Chapter 4: Linear Inequalities in One Variable
  • Chapter 5: Polynomials

📚 Learning Objectives

By the end of this week, you should be able to:

  • Solve and graph linear inequalities in one variable
  • Understand and use inequality and interval notation
  • Identify, classify, add, subtract, and multiply polynomials
  • Apply the distributive property and combine like terms
  • Use polynomial operations in real-world problem-solving

🔢 Part 1: Practice Problems

Chapter 4 – Linear Inequalities in One Variable

  1. Solve the following inequalities. Graph the solution and write it in interval notation:
    a. 4x−3<94x – 3 < 94x−3<9
    b. 2x+53≥1\frac{2x + 5}{3} \geq 132x+5​≥1
    c. −2(x−4)≤6-2(x – 4) \leq 6−2(x−4)≤6
  2. Word Problem:
    A gym membership costs $30 per month, and you have a budget of no more than $200. Write and solve an inequality to determine how many full months you can afford the membership.

Chapter 5 – Polynomials

  1. Identify the degree and leading term of each polynomial:
    a. 3×4−5×2+23x^4 – 5x^2 + 23×4−5×2+2
    b. 7x−4×3+97x – 4x^3 + 97x−4×3+9
    c. −6-6−6
  2. Add or subtract the polynomials:
    a. (2×2+3x+4)+(x2−x+6)(2x^2 + 3x + 4) + (x^2 – x + 6)(2×2+3x+4)+(x2−x+6)
    b. (5×3−2x+1)−(3×3+4x−5)(5x^3 – 2x + 1) – (3x^3 + 4x – 5)(5×3−2x+1)−(3×3+4x−5)
  3. Multiply the polynomials:
    a. (x+2)(x+5)(x + 2)(x + 5)(x+2)(x+5)
    b. (2x−3)(x2+x+1)(2x – 3)(x^2 + x + 1)(2x−3)(x2+x+1)
  4. Real-world application:
    The area of a rectangle is given by the polynomial A=(2x+3)(x−1)A = (2x + 3)(x – 1)A=(2x+3)(x−1).
    a. Multiply to find the simplified expression for area.
    b. What is the area when x=4x = 4x=4?

💬 Part 2: Discussion Prompt

Inequalities and polynomials may seem like just algebra topics, but they show up in many real-life scenarios.

Think of a situation where a polynomial expression might represent a real-world problem (e.g., calculating area, budgeting, or modeling growth). Describe the situation and what the polynomial represents.

Then share an example where you’d use an inequality to set a limit, make a decision, or stay within a budget.

📅 Due Dates

  • Part 1 (Practice Problems): Due
  • Part 2 (Discussion):
    • Initial post by
    • Replies to two classmates by
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