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

Verified step by step guidance

1. Identify the given expression: \(4|x| + \frac{4|y|}{|x|}\).
2. Substitute the given values \(x = -4\) and \(y = 2\) into the expression, remembering to use the absolute values: \(4|{-4}| + \frac{4|2|}{|{-4}|}\).
3. Calculate the absolute values: \(|{-4}| = 4\) and \(|2| = 2\), so the expression becomes \(4 \times 4 + \frac{4 \times 2}{4}\).
4. Perform the multiplications and division separately: \(16 + \frac{8}{4}\).
5. Simplify the fraction and then add the results: \(16 + 2\).

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−4| equals 4, and |2| equals 2. Understanding absolute value is essential for correctly evaluating expressions involving |x| and |y|.

Order of Operations

Order of operations dictates the sequence in which parts of a mathematical expression are evaluated, typically following PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Correctly applying this ensures accurate calculation of expressions like 4|x| + 4|y| / |x|.

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. Here, x = -4 and y = 2 must be substituted into the expression before simplifying. This step is crucial for evaluating the expression numerically.