Question

show a solution to |r| < 4
share your response with your classmates
discuss:
are any points incorrect?
are any solutions missing?

Explanation:

Step1: Apply absolute value inequality rule

For \(|x|0\)), the solution is \(-a < x < a\). Here \(a = 4\), so \(-4 < r < 4\).

Step2: Analyze on the number - line

The number - line should have open circles at \(-4\) and \(4\) (since the inequality is strict, i.e., \(<\) not \(\leq\)) and the line segment between them shaded.

Answer:

The solution of \(|r|<4\) is \(-4 < r < 4\). If we consider the number - line in the problem:

• Points: If there are no open circles at \(-4\) and \(4\), then the representation of the endpoints is incorrect.
• Solutions: The set of all real numbers \(r\) such that \(-4 < r < 4\) should be represented. If only some discrete points (e.g., only integers \(-3,-2,\cdots,3\)) are shown instead of the continuous interval \((-4,4)\), then solutions are missing.