Math Problem Statement
Solution
The number line in the image shows the solution to an absolute value inequality. The endpoints are at and , and the region between them is shaded, indicating the values of that satisfy the inequality.
To write the absolute value inequality that represents this graph, you can follow these steps:
- The center of the interval is the midpoint between and , which is 0.
- The distance from the center (0) to either endpoint (2 or ) is 2.
Thus, the absolute value inequality that describes the graph is:
This inequality means that the distance of from 0 is less than or equal to 2, which matches the shaded region between and on the graph.
Do you need further details or explanations? Here are five related questions to expand on this concept:
- How would you write an absolute value inequality for a range between -5 and 5?
- What would change in the inequality if the points were open circles instead of closed?
- How can you express the same inequality without using absolute value?
- What is the general form of an absolute value inequality for a range between and ?
- How would the inequality change if the interval was shifted to the right?
Tip: The absolute value inequality describes all values of within units of .
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Inequalities
Formulas
|x - c| ≤ r
Theorems
Absolute Value Inequality Theorem
Suitable Grade Level
Grades 7-9