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

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 \(-3(-4) + 4(2)\).
3. Calculate \(-3(-4)\), which involves multiplying \(-3\) by \(-4\).
4. Calculate \(4(2)\), which involves multiplying \(4\) by \(2\).
5. Add the results of the two calculations together and take the absolute value of the sum.

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, |5| = 5 and |-5| = 5. Understanding absolute value is crucial for evaluating expressions that involve both positive and negative outcomes.

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 + 4y|. This step is essential for simplifying the expression to a numerical value, allowing for further calculations.

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 + 4y| is linear in terms of x and y. Understanding how to manipulate and evaluate linear expressions is fundamental in algebra, as it forms the basis for more complex equations.