Math Problem Statement

Solve plot and inteveral test

Solution

The plot shows the solution for the inequality:

x(,5](3,1]x \in (-\infty, -5] \cup (-3, 1]

  • The blue line represents the interval (,5](-∞, -5].
  • The red line represents the interval (3,1](-3, 1].

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Related Questions:

  1. How do absolute value inequalities affect the solution sets?
  2. What is the general method to solve inequalities involving absolute values?
  3. How can inequalities be represented graphically?
  4. What happens if we have strict inequalities (e.g., << instead of \leq)?
  5. How can we check the correctness of our solution by substituting values?

Tip:

When solving inequalities with absolute values, always consider both cases of the absolute value to ensure all possible solutions are found.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Graphical Representation of Inequalities

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12