Problem 25 - College Algebra

Question

evaluate each algebraic expression for \(x=2\) and \(y=-5\) $$ |x+y| $$

Step-by-Step Solution

Answer

The value of the expression |x+y| for x=2 and y=-5 is 3.

Step 1: Substitution

Replace the variables x and y in the algebraic expression with their given values. In this case, substitute x with 2 and y with -5. This will give: |2 + (-5)|.

Step 2: Perform the Operation

Perform the operation inside the absolute value brackets, which is addition in this case. 2 + (-5) = -3.

Step 3: Determine the Absolute Value

Find the absolute value of -3, which gives: |-3| = 3, because the absolute value of a number is its distance from zero on the number line, which is always positive.

Key Concepts

Algebraic Expression Evaluation

Evaluating an algebraic expression involves substituting values for the variables and performing the necessary operations. When given an expression, such as \(|x+y|\), our task is to evaluate it at specific values for \(x\) and \(y\). This starts with replacing each variable with the values provided.

• In algebra, expressions are combinations of numbers, variables, and operations.
• Evaluating means calculating the value of the expression for given values of the variables.

Breaking down the process:- Identify the variables and their given values. For example, here we have \(x = 2\) and \(y = -5\).- Substitute these values into the expression, replacing \(x\) and \(y\). This changes the expression to \(|2 + (-5)|\).- Perform the operations as specified by the expression.Remember, thorough evaluation can help ensure clarity and accuracy when working through math problems.

Substitution in Equations

Substitution is a fundamental step in solving equations or simplifying expressions. It involves replacing variables with their corresponding numerical values. This process makes an otherwise abstract expression more concrete, allowing for direct calculation.

• Choose values to substitute into the expression. These are often provided or solved for in previous problems.
• Carefully replace every instance of the variable in the expression with the given number. Attention to the signs (positive or negative) is crucial.

In our example, after substituting \(x = 2\) and \(y = -5\), our expression becomes \(2 + (-5)\). - Note that we replace \(x\) with 2 and \(y\) with -5 directly inside the absolute value notation.Effective substitution is vital, as each replacement moves you closer to evaluating the expression fully.

Basic Algebra Operations

Basic algebra operations are the building blocks of more complex mathematical processes. They include addition, subtraction, multiplication, and division. Understanding these operations helps in manipulating and solving equations and expressions.

• Perform like operations together following the order of operations (PEMDAS/BODMAS).
• Watch for signs when combining integers, especially when dealing with negatives.

With our expression \(2 + (-5)\):- Addition here involves summing a positive number (2) and a negative number (-5).- The result, \(-3\), is what you get following these operations.- From here, apply the absolute value operation, as required.Ultimately, mastering basic operations allow us to simplify and evaluate expressions efficiently and accurately.