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

Verified step by step guidance

1. Substitute the given values into the expression: replace \(x\) with \(-4\) and \(y\) with \(2\).
2. The expression becomes \(|3(-4) - 2(2)|\).
3. Calculate the multiplication: \(3 \times (-4) = -12\) and \(2 \times 2 = 4\).
4. Substitute these results back into the expression: \(|-12 - 4|\).
5. Simplify the expression inside the absolute value: \(-12 - 4\) and then take the absolute value of the result.

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|, and is always non-negative. For example, |3| = 3 and |-3| = 3. In the context of the expression |3x - 2y|, it indicates that we will take the positive value of the result after substituting x and y.

Substitution

Substitution is the process of replacing variables in an expression with their corresponding numerical values. In this case, we substitute x = -4 and y = 2 into the expression 3x - 2y. This step is crucial for evaluating the expression accurately and allows us to simplify it to a numerical value.

Linear Expressions

A linear expression is an algebraic expression in which each term is either a constant or the product of a constant and a single variable raised to the first power. The expression 3x - 2y is linear because it involves the variables x and y to the first degree. Understanding linear expressions is essential for evaluating and manipulating them in algebra.