Math Problem Statement

-[-5]-[5]

Solution

The interval [5,5][-5, 5] refers to the set of all real numbers between -5 and 5, inclusive of both endpoints. In interval notation, square brackets [][ ] mean that the endpoints are included.

Key features of the interval [5,5][-5, 5]:

  • It includes both -5 and 5 (because of the square brackets).
  • Any real number xx within this range satisfies 5x5-5 \leq x \leq 5.
  • This interval contains all real numbers between -5 and 5, such as 4,2,0,3.5-4, -2, 0, 3.5, etc.

Would you like a deeper explanation of intervals or how they're used?

Here are five related questions to expand on this concept:

  1. How would the interval look if it only included numbers between -5 and 5 but excluded the endpoints?
  2. What is the difference between open and closed intervals?
  3. How would you represent a half-open interval from -5 to 5?
  4. Can you define the interval using set-builder notation?
  5. What is the length of the interval [5,5][-5, 5]?

Tip: In interval notation, round brackets ()( ) are used to exclude endpoints, while square brackets [][ ] are used to include them.

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Math Problem Analysis

Mathematical Concepts

Real Numbers
Intervals
Inequalities

Formulas

Interval Notation: [a, b] denotes all real numbers between a and b inclusive.
Inequality: a ≤ x ≤ b, where x is a real number.

Theorems

Fundamental Theorem of Real Numbers on Intervals

Suitable Grade Level

Grades 6-8