Math Problem Statement

Is your friend correct in solving the inequality 8 ≤ x + 3 and graphing the solution?

Solution

From the uploaded image, your friend's solution involves solving the inequality 8x+38 \leq x + 3 and graphing the solution. Here's the step-by-step reasoning:

  1. Solve the inequality:

    • Start with 8x+38 \leq x + 3.
    • Subtract 3 from both sides: 83x8 - 3 \leq x.
    • Simplify: 5x5 \leq x, or equivalently x5x \geq 5.
  2. Check the graph:

    • The solution x5x \geq 5 should be represented as a line starting at 5 (inclusive, so the point at 5 should be solid) and extending to the right.
    • The graph provided shows this correctly.

Based on the inequality and the graph in the image, your friend's solution and graph are correct.

If you mistakenly chose "No" and need clarification, let me know if you need further assistance!


Here are five follow-up questions to explore this topic:

  1. What are the common mistakes people make when solving linear inequalities?
  2. How can you verify the correctness of a graphed inequality solution?
  3. What is the significance of an inclusive inequality (e.g., \leq or \geq) in graphing solutions?
  4. Can you provide another example of solving and graphing a similar inequality?
  5. How does solving compound inequalities differ from single-variable inequalities?

Tip: Always double-check the inequality sign when solving and graphing to ensure the solution matches the problem statement!

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Graphing Inequalities

Formulas

Simplifying linear inequalities by isolating the variable

Theorems

Properties of inequality operations

Suitable Grade Level

Grades 6-8