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

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Identify the given expression: \(|x| + |y|\), where \(x = 2\) and \(y = -5\).

Recall that the absolute value function \(|a|\) gives the non-negative value of \(a\), so \(|a| = a\) if \(a \geq 0\), and \(|a| = -a\) if \(a < 0\).

Calculate \(|x|\) by substituting \(x = 2\). Since 2 is positive, \(|2| = 2\).

Calculate \(|y|\) by substituting \(y = -5\). Since -5 is negative, \(|-5| = -(-5) = 5\).

Add the results: \(|x| + |y| = 2 + 5\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |x| equals x if x is positive or zero, and -x if x is negative. This concept is essential for evaluating expressions like |x| + |y|.

Substitution in Algebraic Expressions

Substitution involves replacing variables in an expression with given numerical values. Here, x and y are replaced with 2 and -5 respectively, allowing the expression to be evaluated numerically. This step is crucial for solving or simplifying algebraic expressions.

Evaluating Algebraic Expressions

Evaluating an algebraic expression means calculating its value after substituting variables with specific numbers. It requires following the order of operations and correctly applying arithmetic rules to find the final numerical result.

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