Math Problem Statement

answer

Consider the following subset of the real number line. How can this set be expressed using inequalities?

Solution

Looking at the provided number line, the shaded region extends from 4-4 to 1-1. The circle at 4-4 is closed, meaning 4-4 is included in the set, and the circle at 1-1 is open, meaning 1-1 is not included.

The correct inequality to express this set is: 4x<1-4 \leq x < -1

Thus, the correct answer is option c.) 4x<1-4 \leq x < -1.

Would you like more details on why this inequality notation is used? Here are some related questions you might explore:

  1. What is the difference between open and closed intervals on a number line?
  2. How are inequalities used to represent intervals?
  3. How would the inequality change if both circles were open?
  4. Can you graph an inequality with both closed endpoints?
  5. What is interval notation, and how does it relate to inequalities?

Tip: Remember, a closed circle on a number line means the endpoint is included, and an open circle means it’s not!

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Math Problem Analysis

Mathematical Concepts

Inequalities
Real Number Line
Intervals

Formulas

Inequalities: a ≤ x < b
Set notation: {x | a ≤ x < b}

Theorems

The definition of inequalities on a real number line
Interval notation and open/closed intervals

Suitable Grade Level

Grades 6-8