Math Problem Statement

Matching inequalities with their respective number line representations.

Solution

The image you uploaded appears to contain number lines along with inequalities related to values of xx. These inequalities are represented in different forms, and each corresponds to a certain range of values for xx.

The number lines show:

  1. A range where 5x5-5 \leq x \leq 5.
  2. The inequality 0<x0 < x suggests that xx is strictly positive.
  3. The inequality x<0x < 0 represents negative values of xx.
  4. The inequality x0x \geq 0 corresponds to all values of xx that are non-negative (zero or positive).
  5. The inequality 0x0 \geq x represents values of xx that are non-positive (zero or negative).

Would you like a more detailed explanation of how these inequalities and ranges work? Or do you need help with a specific problem related to this image? Let me know!

Here are five questions that might help deepen your understanding:

  1. How do we graph the inequality x0x \geq 0 on a number line?
  2. What’s the difference between a strict inequality (like x>0x > 0) and a non-strict inequality (like x0x \geq 0)?
  3. How do you solve compound inequalities like x>0 and x<3x > 0 \text{ and } x < 3?
  4. Can you explain how to represent a number range, such as x(2,3]x \in (-2, 3], on a number line?
  5. What are the steps to solving an inequality like 2x532x - 5 \geq 3?

Tip: When graphing inequalities on a number line, use a closed circle for "greater than or equal to" and "less than or equal to" and an open circle for strict inequalities ("greater than" or "less than").

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Math Problem Analysis

Mathematical Concepts

Inequalities
Number Line Representation

Formulas

Inequality notation: <, >, ≤, ≥

Theorems

Graphing inequalities on a number line

Suitable Grade Level

Grades 6-9