Evaluate each expression for x = -4 and y = 2. |2x - 5y|

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 $|2(-4)-5(2)|$.
3. Calculate the multiplication: $2\times (-4)=-8$ and $5\times 2=10$.
4. Substitute these values back into the expression: $|-8-10|$.
5. Simplify the expression inside the absolute value: $-8-10=-18$, then take the absolute value: $|-18|=18$.

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. Understanding absolute value is crucial for evaluating expressions that involve both positive and negative outcomes.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. In this case, we substitute x = -4 and y = 2 into the expression |2x - 5y|. This step is essential for simplifying the expression to a numerical value, allowing for further evaluation.

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 2x - 5y is linear, and understanding how to manipulate and evaluate such expressions is fundamental in algebra. Evaluating linear expressions involves performing arithmetic operations according to the order of operations.