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

Verified step by step guidance

1. Identify the absolute values: \(|x|\) and \(|y|\).
2. Calculate \(|x|\) by taking the absolute value of \(x = -4\), which is \(4\).
3. Calculate \(|y|\) by taking the absolute value of \(y = 2\), which is \(2\).
4. Substitute \(|x| = 4\) and \(|y| = 2\) into the expression \(4|x| + \frac{4|y|}{|x|}\).
5. Simplify the expression by performing the operations: \(4 \times 4 + \frac{4 \times 2}{4}\).

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|. For example, |−4| equals 4, and |2| equals 2. 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. Properly applying these rules is essential for accurately evaluating complex expressions.

Evaluating Expressions

Evaluating an expression involves substituting specific values for variables and performing the necessary calculations. In this case, substituting x = -4 and y = 2 into the expression requires careful handling of absolute values and following the order of operations. This process is fundamental in algebra for simplifying and solving equations.