To determine whether to use a fraction for an answer and whether to use a closed or open circle on a number line, we need to consider the context of the problem, particularly if it involves inequalities.
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Fraction as an Answer: If the solution to a problem can be expressed as a fraction, then it is perfectly acceptable to represent the answer that way. For example, if the solution to an equation is \( \frac{1}{2} \), that is a valid answer.
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Open vs. Closed Circle:
- Closed Circle: Use a closed circle on a number line when the endpoint of an inequality is included in the solution. This corresponds to "less than or equal to" (≤) or "greater than or equal to" (≥).
- Open Circle: Use an open circle when the endpoint is not included in the solution. This is the case for "less than" (<) or "greater than" (>).
For example:
- For the inequality \( x < \frac{1}{2} \), you would use an open circle at \( \frac{1}{2} \).
- For the inequality \( x \leq \frac{1}{2} \), you would use a closed circle at \( \frac{1}{2} \).
If you have a specific inequality or equation in mind, I can give more tailored guidance.