Math Problem Statement

Match the statements defined below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.

Solution

Let's analyze and solve this problem. The task is to match each statement with its corresponding mathematical expression.

Here are the statements and expressions:

Statements:

  1. xx is less than or equal to 4.
  2. xx is greater than 4.
  3. xx is any real number.
  4. xx is greater than or equal to 4.
  5. xx is less than 4.

Expressions:

  • A. x4x \geq 4
  • B. 4<x4 < x
  • C. x<4x < 4
  • D. x4x \leq 4
  • E. <x<-\infty < x < \infty (this represents all real numbers)

Matching:

  1. xx is less than or equal to 4: This matches D (x4x \leq 4).
  2. xx is greater than 4: This matches B (4<x4 < x).
  3. xx is any real number: This matches E (<x<-\infty < x < \infty).
  4. xx is greater than or equal to 4: This matches A (x4x \geq 4).
  5. xx is less than 4: This matches C (x<4x < 4).

Final Answer:

  1. D
  2. B
  3. E
  4. A
  5. C

Would you like further details on any part of this solution, or do you have any questions?

Here are 5 related questions for you to explore:

  1. What is the difference between x>4x > 4 and x4x \geq 4?
  2. How do we represent all real numbers using inequalities?
  3. What is the interpretation of -\infty and \infty in inequalities?
  4. How can inequalities be graphed on a number line?
  5. How do compound inequalities work?

Tip:

When matching inequalities, always pay attention to whether the statement includes equality (like \geq or \leq) or strictly compares values (like >> or <<).

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Math Problem Analysis

Mathematical Concepts

Inequalities
Real Numbers
Set Notation

Formulas

Inequalities such as x <= 4, x > 4

Theorems

Properties of inequalities and number sets

Suitable Grade Level

Grades 9-11