In Exercises 61–66, evaluate each algebraic expression for x=2 and y=-5. |x+y|

Verified step by step guidance

1. Identify the given expression: \(|x + y|\).
2. Substitute the given values into the expression: \(x = 2\) and \(y = -5\).
3. Perform the addition inside the absolute value: \(2 + (-5)\).
4. Calculate the result of the addition: \(-3\).
5. Apply the absolute value to the result: \(|-3|\).

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|. For example, |3| equals 3, and |-3| also equals 3. In the context of the expression |x+y|, it indicates that we will consider the non-negative result of the sum of x and y.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. In this case, we substitute x with 2 and y with -5 in the expression x+y. This step is crucial for evaluating the expression accurately, as it transforms the algebraic expression into a numerical one.

Evaluating Expressions

Evaluating an expression involves performing the necessary arithmetic operations to simplify it to a single numerical value. After substituting the values of x and y into the expression x+y, we will compute the result and then apply the absolute value to find the final answer. This process is fundamental in algebra for solving equations and expressions.