Math Problem Statement

Write an absolute value inequality for the graph below. Use x for your variable.

Solution

From the graph you provided, we see two open circles at x=2x = -2 and x=2x = 2, which indicate that these values are not included in the solution. The values in between, however, are included. This suggests that the variable xx can take any value between -2 and 2, exclusive.

The absolute value inequality that represents this graph is: x<2|x| < 2

This inequality states that the absolute value of xx must be less than 2, which corresponds to the range of values for xx from -2 to 2, not including the endpoints themselves.

Would you like any further details on this or have any questions about absolute value inequalities?

Here are some related questions you might find helpful:

  1. How would the inequality change if the circles on the graph were closed?
  2. What would be the inequality if xx values were greater than 2 and less than -2?
  3. How do we solve absolute value inequalities algebraically?
  4. Can you explain why absolute values are used in inequalities?
  5. How would this inequality be graphed on a coordinate plane?

Tip: When writing absolute value inequalities from a number line graph, always check whether the circles are open or closed to determine if the endpoints are included in the inequality.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value
Inequalities

Formulas

|x| < a

Theorems

Absolute Value Inequalities

Suitable Grade Level

Grades 6-8