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

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Identify the given expression and the values of the variables: the expression is \(|3x - 2y|\), with \(x = -4\) and \(y = 2\).

Substitute the values of \(x\) and \(y\) into the expression: replace \(x\) with \(-4\) and \(y\) with \(2\) to get \(|3(-4) - 2(2)|\).

Simplify inside the absolute value by performing the multiplication: calculate \(3 \times (-4)\) and \(2 \times 2\) to get \(|-12 - 4|\).

Combine the terms inside the absolute value: simplify \(-12 - 4\) to get \(|-16|\).

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.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.