Evaluate each expression for x = -4 and y = 2. 2|y| - 3|x| / |xy|

Verified step by step guidance

1. Substitute the given values into the expression: replace \(x\) with \(-4\) and \(y\) with \(2\).
2. Calculate the absolute values: \(|y| = |2|\) and \(|x| = |-4|\).
3. Calculate the product \(xy\) and then find its absolute value: \(|xy| = |-4 \times 2|\).
4. Substitute the absolute values back into the expression: \(2|y| - 3|x| / |xy|\).
5. Simplify the expression by performing the arithmetic operations: multiplication, division, and subtraction.

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

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. Correctly applying these rules is essential for accurately evaluating complex expressions.

Substitution

Substitution involves replacing variables in an expression with their corresponding numerical values. In this case, x = -4 and y = 2 must be substituted into the expression before evaluation. This step is fundamental in simplifying expressions and solving equations, allowing for the calculation of specific values based on given inputs.