Math Problem Statement

Which expressions represent this interval? Select all that apply.

Solution

The interval represented on the number line is from 4-4 to 33, where 4-4 is included (denoted by the filled circle) and 33 is not included (denoted by the open circle). Let's analyze each expression to see if it represents this interval:

  • A. 4x<3-4 \leq x < 3: This is correct because it means xx is between 4-4 and 33, including 4-4 but excluding 33, which matches the graph.

  • B. 4<x3-4 < x \leq 3: This is incorrect because it excludes 4-4 (the open inequality) and includes 33, which doesn't match the number line.

  • C. (4,3)(-4, 3): This is incorrect because this notation excludes both 4-4 and 33, whereas the graph includes 4-4.

  • D. [4,3)[-4, 3): This is correct because this notation means xx is between 4-4 and 33, including 4-4 and excluding 33, which matches the graph.

  • E. {xx is greater than 4}\{x \mid x \text{ is greater than } -4\}: This is incorrect because it implies that xx is strictly greater than 4-4, excluding 4-4, which doesn't match the number line.

So, the correct answers are A and D.

Would you like further clarification on any of these? Here are some related questions for more practice:

  1. How would you write the interval if both 4-4 and 33 were included?
  2. What does the notation (4,3](-4, 3] represent?
  3. How would you describe the set of numbers {xx<3}\{x \mid x < 3\}?
  4. What is the difference between open and closed intervals in terms of notation?
  5. How would the inequality look if neither 4-4 nor 33 were included?

Tip: When dealing with intervals, pay close attention to the type of bracket or inequality. Square brackets [][ \, ] mean the value is included, while parentheses ()( \, ) mean the value is excluded.

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Math Problem Analysis

Mathematical Concepts

Intervals
Inequalities
Set Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9