Simplify:
$|15-4|=$
The given expression is \(|15 - 4|\). The absolute value function, denoted by \(|x|\), represents the distance of a number \(x\) from zero on the number line, regardless of its direction. It is defined as \(|x| = x\) if \(x \ge 0\) and \(|x| = -x\) if \(x < 0\). Our goal is to evaluate this expression step by step.
First, we perform the subtraction inside the absolute value bars:
\[15 - 4 = 11\]
Now, we apply the absolute value to the result:
\[|11| = 11\]
Since \(11 \ge 0\), the absolute value of 11 is simply 11 itself.
Comparing the result with the given choices:
The correct value is \(11\). Thus, we conclude that \(|15 - 4| = \boxed{11}\).
Absolute values are widely used in everyday life to measure differences regardless of direction or order. For example, if you are tracking the difference in temperature between two cities, say \(15^\circ \text{C}\) and \(4^\circ \text{C}\), you want to know how far apart these temperatures are on the thermometer. By calculating \(|15 - 4| = 11^\circ \text{C}\), you determine the absolute difference in temperature, which is a positive value representing the magnitude of the gap between the two readings.