Math Problem Statement

Write the following set as an interval using interval notation.

{x|7<x≤9}

Solution

The set {x7<x9}\{x \mid 7 < x \leq 9\} in interval notation is:

(7,9](7, 9]

This represents all values of xx that are greater than 7 but less than or equal to 9.

Would you like more details on how interval notation works, or do you have any other questions?

Here are five related questions:

  1. How do you write the set {x3x<8}\{x \mid 3 \leq x < 8\} in interval notation?
  2. What does the interval [2,6)[2, 6) represent on a number line?
  3. How do you represent the set of all real numbers less than or equal to 5 using interval notation?
  4. What is the interval notation for the set {x4<x<1}\{x \mid -4 < x < 1\}?
  5. How do you express the union of two intervals, such as (2,5](2, 5] and [6,9)[6, 9)?

Tip: Square brackets [][ ] in interval notation indicate that the endpoint is included, while parentheses ()( ) indicate that it is not.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Interval Notation
Inequalities

Formulas

Interval notation representation
Inequality representation of sets

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 6-8