Find each sum or difference. See Example 1.|-8 - 6|

Verified step by step guidance

1. Identify the expression inside the absolute value: \(-8 - 6\).
2. Calculate the expression inside the absolute value: \(-8 - 6 = -14\).
3. Apply the absolute value operation: \(|-14|\).
4. Recall that the absolute value of a number is its distance from zero on the number line, which is always positive.
5. Thus, the absolute value of \(-14\) is \(14\).

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |−8| equals 8, and |−6| equals 6, as both values are 8 and 6 units away from zero, respectively.

Operations with Absolute Values

When performing operations involving absolute values, it is essential to first evaluate the absolute values of the individual numbers before applying any arithmetic operations. For instance, in the expression |−8 - 6|, you would first calculate the result of −8 - 6, which equals −14, and then find the absolute value, resulting in |−14| = 14.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the context of absolute values, it is crucial to follow these rules to correctly evaluate expressions involving multiple operations.