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The absolute value of a number is a fundamental concept in mathematics. It measures how far a number is from zero on a number line, without considering the direction. Essentially, the absolute value of a number is always non-negative. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5. In mathematical notation, the absolute value of a number \( p \) is expressed as \(|p|\). Whether \( p \) is positive or negative, the absolute value \(|p|\) provides its distance from 0.

Solving equations that involve absolute values might seem daunting at first, but once you understand the concept, it becomes straightforward. When you are given an equation like \( |p| = 0 \), you need to determine the values of \( p \) that make this equation true.

The key to solving this type of equation lies in understanding that the absolute value represents a distance. Since no distance can be negative, the only scenario where the absolute value of a number is zero is when the number itself is zero.

Thus, the solution to the equation \( |p| = 0 \) is simply \( p = 0 \). This conclusion is based on the fact that the distance from zero to zero is zero and no other number can satisfy this condition.

Understanding distance on a number line will make it easier to grasp the concept of absolute value.

Imagine a straight line with zero at the center. Positive numbers like 1, 2, and 3 are to the right of zero, while negative numbers like -1, -2, and -3 are to the left.

The distance of any point on this line from zero is what we call the absolute value. For instance, the number 4 is 4 units away from zero, so its absolute value is 4. Similarly, the number -4 is also 4 units away from zero, so its absolute value is also 4.

This concept applies directly when solving absolute value equations. If you need to find when \( |p| = 0 \), you are essentially looking for a number whose distance from zero is zero. Clearly, the only number that fits this description is zero itself.