Is -3 true for p ≤ -2? If false, write a sample solution set with 3 numbers.
The problem asks to evaluate whether the statement that \(-3\) is a solution to the inequality \(p < 2 - 2\) is true or false. First, we simplify the given inequality:
\[p < 2 - 2\]
\[p < 0\]
We are testing if \(p = -3\) satisfies this condition. Substituting \(-3\) for \(p\):
\[-3 < 0\]
Since \(-3\) is indeed less than \(0\), the statement is true.
We have verified that the inequality \(p < 2 - 2\) simplifies to \(p < 0\). Substituting \(p = -3\) into this inequality results in the expression \(-3 < 0\), which is a correct mathematical statement. Therefore, the value \(-3\) is indeed a solution to the inequality \(p < 2 - 2\). Since the statement is true, no further set of numbers is required. The final conclusion is that the statement is true.
Understanding inequalities is fundamental to programming and resource management. For example, if you are writing a piece of software that checks if a patient's temperature is below a certain threshold (like \(0^\circ \text{C}\) for freezing point or a specific physiological limit), you use inequalities to define the safe range. In this case, checking if \(-3 < 0\) is like confirming that a temperature reading of \(-3^\circ \text{C}\) safely meets the condition of being below freezing point. Mastering these logical evaluations ensures that your code or logic handles data points correctly.