Math Problem Statement

Write down the inequality shown on the number line.

Solution

The number line shows an open circle at y=3y = -3 and a closed circle at y=2y = 2, with a line connecting them, indicating the interval.

  • The open circle at y=3y = -3 means that this value is not included in the solution.
  • The closed circle at y=2y = 2 means that this value is included in the solution.

Thus, the inequality that represents the number line is: 3<y2-3 < y \leq 2

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

  1. How do you represent inequalities on a number line when both endpoints are closed?
  2. What changes in the inequality if the open circle is replaced with a closed circle?
  3. How can you express the inequality 3<y2-3 < y \leq 2 in interval notation?
  4. How do you solve an equation with a compound inequality?
  5. What does it mean for a number to satisfy a strict inequality versus a non-strict inequality?

Tip: Remember that open circles on a number line mean the endpoint is not included (strict inequality), while closed circles mean the endpoint is included (non-strict inequality).

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Math Problem Analysis

Mathematical Concepts

Inequalities
Number Line Representation

Formulas

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Theorems

Inequality Theorem

Suitable Grade Level

Grades 6-8