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Absolute values are a way to measure how far a number is from zero on the number line, regardless of direction. They are always non-negative. The absolute value of a number, denoted by vertical bars (e.g., \(|-1|\)), is essentially the value of the number without considering its sign.

For instance:

• \(|-1| = 1\)
• \(|-10| = 10\)
• \(|7| = 7\)

Absolute values are especially useful when dealing with tasks such as addition and subtraction of negative numbers, because they let us consider only the size of each number. In addition problems involving negative numbers, you often add the absolute values to find the magnitude of the total, then determine the sign based on the original numbers.

Negative numbers are values less than zero, often represented with a minus sign (-) in front. These numbers can often trip up calculations if you are not careful about their properties, especially during operations like addition and subtraction.

When adding two negative numbers, like \(-1\) and \(-10\):

• Add their absolute values: \(1 + 10 = 11\)
• Since both numbers are negative, the result is negative: \(-11\)

Negative numbers represent values below zero, used frequently in contexts like temperatures below freezing, financial debts, and more. When working with them, it's important to understand how signs affect mathematical operations.

Parentheses are used in math to indicate that the operations inside them should be performed first. This comes from the order of operations, often remembered by the PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)) rule.

In the given problem, \(-1 + (-6 - 4)\), the expression inside the parentheses is simplified first. This involves straightforward subtraction.

• Calculate \(-6 - 4\): The subtraction of a positive 4 from a negative 6 gives \(-10\).

Once simplified, the expression becomes \(-1 + (-10)\), which can then be solved using rules for adding negative numbers as discussed. Parentheses help organize complex expressions and guide the order in which operations are conducted, ensuring clarity and accuracy in calculations.