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

Verified step by step guidance

1. Identify the given expression and the values of the variables: the expression is \(|3x - 2y|\), with \(x = -4\) and \(y = 2\).
2. Substitute the values of \(x\) and \(y\) into the expression: replace \(x\) with \(-4\) and \(y\) with \(2\) to get \(|3(-4) - 2(2)|\).
3. Simplify inside the absolute value by performing the multiplication: calculate \(3 \times (-4)\) and \(2 \times 2\) to get \(|-12 - 4|\).
4. Combine the terms inside the absolute value: simplify \(-12 - 4\) to get \(|-16|\).
5. Evaluate the absolute value: recall that the absolute value of a number is its distance from zero, so \(|-16|\) equals the positive value of 16.

Key Concepts

Substitution in Algebraic Expressions

Substitution involves replacing variables in an expression with given numerical values. This is the first step in evaluating expressions, allowing you to simplify and calculate the result accurately.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Following this ensures correct evaluation of expressions.

Absolute Value

Absolute value represents the distance of a number from zero on the number line, always yielding a non-negative result. It is denoted by vertical bars, e.g., |x|, and affects the final value after evaluating the expression inside.