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Understanding absolute value is crucial when dealing with both positive and negative numbers. The absolute value of a number refers to its distance from zero on the number line, without considering its direction. It's always a non-negative number.
For example, the absolute value of

• 2 is 2, since 2 is 2 units away from zero.
• -3 is 3, because -3 is also 3 units from zero, but in the opposite direction.

To denote absolute value, we use vertical bars. As in the exercise \(|2 - 10|\), we first perform the operation inside the bars. After calculating \(2 - 10 = -8\), we take \(|-8|\), which equals 8.

Subtraction is one of the basic arithmetic operations. It involves taking one quantity away from another. In simple terms, if you have a number and you subtract another number from it, you find out how much is left or how much one number exceeds another.
In the subtraction problem \(a - b\),

• \(a\) is called the minuend, and
• \(b\) is the subtrahend.

To perform \(a - b\), you find the point on the number line that is \(b\) units to the left of \(a\). When both numbers are positive, it's simply counting back. However, when negative numbers are involved, subtraction can often mean adding the absolute value, especially when subtracting a negative number.
In our exercise, after finding the absolute value result to replace \(|2 - 10|\) with 8, we complete \(-9 - 8\), equating to \(-17\).

Negative numbers are numbers less than zero. They are used to represent opposite positions or deficits. On the number line, negative numbers are found to the left of zero — the greater the negative number, the further left it is.
They can sometimes be tricky, especially when mixed with subtraction or when calculating the absolute value.
Key points on negative numbers:

• Subtracting a positive number is straightforward: \(-9 - 8\) means moving 8 units further left from -9.
• Subtracting a negative number often becomes an addition: \(a - (-b) = a + b\).

In the exercise, after evaluating \(|2 - 10|\) to 8 (a positive number), we subtract it from \(-9\), resulting in the final answer, \(-17\).