Math Problem Statement

Express the interval in​ set-builder notation and graph the interval on a number line. (-4,-1)

Solution

The given interval (4,1)(-4, -1) is an open interval, which means that the endpoints 4-4 and 1-1 are not included.

Set-builder notation:

In set-builder notation, we express the interval as: {xR4<x<1}\{ x \in \mathbb{R} \mid -4 < x < -1 \} This means that xx is a real number such that xx is greater than 4-4 and less than 1-1.

Number line graph:

On the number line, the interval is represented by a line segment between 4-4 and 1-1, with open circles at 4-4 and 1-1 to indicate that these points are not included in the interval.

I can graph this for you if needed. Would you like to see a visual representation of this?

Here are 5 related questions to expand on:

  1. How is a closed interval different from an open interval in set-builder notation?
  2. Can you convert a half-open interval into set-builder notation?
  3. How do you express the union of two intervals in set-builder notation?
  4. How would the graph look if the interval was [4,1][-4, -1]?
  5. How do you express inequalities in set-builder notation?

Tip: In set-builder notation, remember to clearly specify the domain and the condition on the variable (e.g., xRx \in \mathbb{R}).

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Math Problem Analysis

Mathematical Concepts

Set Theory
Intervals
Real Numbers

Formulas

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Theorems

Set-builder notation

Suitable Grade Level

Grades 9-12