Is the inequality $15 < 3$ true or false?
The problem asks us to determine the truth value of the statement \(15 < 3\). This involves comparing two real numbers, 15 and 3, using the "less than" inequality symbol. The notation \(a < b\) indicates that the value \(a\) is strictly to the left of the value \(b\) on the number line, or alternatively, that the difference \(b - a\) is positive.
To determine the truth value, we compare 15 and 3 directly. On the number line, 15 is to the right of 3, which implies \(15 > 3\). Mathematically, we can verify this by calculating the difference \(3 - 15\). The result is \(3 - 15 = -12\). Since \(-12\) is not a positive number, the condition for \(15 < 3\) is not satisfied.
Because 15 is greater than 3, the statement \(15 < 3\) is mathematically incorrect. Therefore, the statement is false. The final answer is \(\boxed{\text{False}}\).
In everyday life, understanding numerical relationships is crucial. For instance, if you are comparing the costs of two items, say a toy that costs \$15 and another that costs \$3, and you are checking if the \$15 toy is cheaper than the \$3 toy, you are essentially evaluating an inequality like \(15 < 3\). Since it is not cheaper, you correctly conclude the statement is false. This helps in making informed financial decisions.