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 and graphing the solution. Here's the step-by-step reasoning:
-
Solve the inequality:
- Start with .
- Subtract 3 from both sides: .
- Simplify: , or equivalently .
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Check the graph:
- The solution 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:
- What are the common mistakes people make when solving linear inequalities?
- How can you verify the correctness of a graphed inequality solution?
- What is the significance of an inclusive inequality (e.g., or ) in graphing solutions?
- Can you provide another example of solving and graphing a similar inequality?
- 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