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The concept of absolute value might seem tricky at first, but it's quite simple once you break it down. The absolute value of a number is the distance between that number and zero on a number line. Distance is always a positive quantity. Therefore, regardless of whether the number is positive or negative, its absolute value will always be positive.
For instance, the absolute value of both 12 and -12 is the same because they are both 12 units away from zero. This can be represented as: \(|12| = 12\) and \(|-12| = 12\).
Understanding this concept is essential because it is used in many areas of mathematics, including equations and inequalities. Knowing how to calculate absolute value helps you solve problems more efficiently.

A number line is a visual representation of numbers arranged in order. It is incredibly useful for understanding absolute value because it helps you see exactly how far a number is from zero.
Imagine a line with zero in the center, positive numbers on the right, and negative numbers on the left. The farther you move to the right, the higher positive numbers you get. The farther you move to the left, the higher negative numbers you get.
An important thing to remember is: distance is always positive. Whether you start from zero and move right to 12 or left to -12, the distance covered is always 12 units. Therefore, the absolute value \(|12|\text{ and } |-12|\) will both be equal to 12.
Using a number line can help you understand not just absolute value but many other algebraic concepts.

Simplifying expressions involves reducing them to their simplest form. This often requires understanding and applying several mathematical concepts, including absolute value.
When you see an expression with an absolute value, like \(-|12|\), you start by solving the absolute value part first. From our earlier examples, \(|12| = 12\). So, you replace the absolute value within the expression, making it easier to deal with.
Next, you apply any operations left in the expression. In this case, you need to add the negative sign, resulting in: \-|12| = -12 \
By following these steps, you make the problem more manageable and easier to solve. Simplifying expressions is a foundation for more advanced mathematical concepts.