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In mathematics, negation essentially means to change the sign of a number. If we start with a positive number, its negation becomes negative, and vice versa. For instance, the negation of 5 is -5, and the negation of -7 is 7. This change in sign can dramatically influence the value, especially when dealing with absolute values.
Remember that the absolute value of a number is always non-negative since it represents the distance from zero. When you apply negation to an absolute value, you end up with a negative number because you are multiplying the non-negative absolute value by -1.
For example, in our exercise, \(-|-2|\) becomes -2 because the absolute value of -2 is 2, and then it is negated to -2.

A number line is a visual representation of numbers along a straight line. This helps students understand the relative position and order of numbers. Zero is typically placed in the center, with positive numbers to the right and negative numbers to the left.
Using a number line makes it easier to compare numbers, especially when dealing with negative values. By visualizing the position of -2 and -3, you can see that -3 is further left than -2, indicating that -3 is lesser than -2.
For this exercise, when we looked at -|-2| and -|-3| on the number line, we noted that -3 is to the left of -2, confirming that -3 is the smaller number.

Comparing values, especially negative numbers, can be tricky. To simplify, always think about the number line. Numbers to the left are smaller, and numbers to the right are larger.
When we compare -|-2| (which simplifies to -2) and -|-3| (which simplifies to -3), we use the number line to help us. We observe that -3 is to the left of -2 on the number line.
Therefore, in terms of comparative value, -3 is less than -2. This exercise reinforces understanding of absolute values and their negation, while also showing how to compare the resulting values.