Evaluate each expression for x = -4 and y = 2. |-8y + x| / -|x|

Verified step by step guidance

1. Substitute the given values into the expression: replace \( x \) with \( -4 \) and \( y \) with \( 2 \).
2. The expression becomes \( |-8(2) + (-4)| / -|-4| \).
3. Calculate the value inside the absolute value in the numerator: \( -8 \times 2 + (-4) = -16 - 4 \).
4. Simplify the expression inside the absolute value: \( |-20| \).
5. Calculate the absolute values and simplify the expression: \( 20 / -4 \).

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, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for evaluating expressions that involve both positive and negative numbers.

Substitution

Substitution is the process of replacing variables in an expression with their given values. In this case, we substitute x = -4 and y = 2 into the expression. This step is essential for simplifying the expression and obtaining a numerical result. Proper substitution ensures that the evaluation reflects the intended values of the variables.

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. Following these rules is vital when evaluating complex expressions to avoid errors in calculations.