Math Problem Statement

a) Enter [3, ∞) in interval notation. b) Enter 2 < x ≤ 7 in inequality notation.

Solution

From the image, it appears that there are two problems where the interval and inequality notations have been entered incorrectly. Let’s address both issues:

a) Enter [3,)[3, ∞) in interval notation

  • The correct interval notation for the expression [3,)[3, ∞) is: [3,)[3, \infty) Where:
    • The square bracket "[" means 3 is included in the interval.
    • The parenthesis ")" after ∞ means the interval goes infinitely and does not include infinity (as infinity is not a real number that can be included).

Mistake in your answer:

You entered: 3<x3 < x This is inequality notation, not interval notation. To express this in correct interval notation, write [3,)[3, \infty).


b) Enter 2<x72 < x \leq 7 in inequality notation

  • The correct inequality notation for the interval (2,7](2, 7] is: 2<x72 < x \leq 7 Where:
    • The inequality "2 < x" indicates that xx is strictly greater than 2 (not including 2).
    • The inequality "x7x \leq 7" means xx is less than or equal to 7 (7 is included).

Mistake in your answer:

You entered: (2,7](2, 7] This is interval notation. To express this in correct inequality notation, use 2<x72 < x \leq 7.


Would you like more details or have any questions? Here are some related questions for further practice:

  1. What is the interval notation for x>5x > 5?
  2. How do you express the interval (,0](-∞, 0] in inequality form?
  3. What is the inequality notation for x(3,8)x \in (-3, 8)?
  4. How do you write x2x \leq -2 in interval notation?
  5. Convert the interval notation [0,4)[0, 4) into an inequality.

Tip: Interval notation uses brackets to show whether endpoints are included or excluded, whereas inequality notation uses comparison symbols like <<, >>, , and .

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Math Problem Analysis

Mathematical Concepts

Inequality Notation
Interval Notation
Real Number Line

Formulas

Interval Notation: (a, b), [a, b], (a, ∞), (-∞, b]
Inequality Notation: a < x ≤ b

Theorems

None

Suitable Grade Level

Grades 6-8