Problem 27 - College Algebra

Question

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

Step-by-Step Solution

Answer

The algebraic expression evaluates to 7 when \(x=2\) and \(y=-5\).

Step 1: Substitute the given values

First, replace the variables with the given values. So the task is to evaluate \(|2| + |-5|\).

Step 2: Evaluate each absolute value

The next step is to calculate the absolute value of the numbers in the expression. The absolute value of 2 is 2, and the absolute value of -5 is 5.

Step 3: Perform the addition

Now that we have the absolute values, perform the addition. So we have \(2 + 5 = 7\).

Key Concepts

Evaluate Algebraic Expressions

When we talk about evaluating algebraic expressions, what we're really discussing is the process of calculating the value of an expression using given numbers for each variable. If you have an expression like \(|x|+|y|\), you need specific values for \(x\) and \(y\) to proceed.

• The goal is to find a numerical answer by the end.
• Algebraic expressions can involve several operations like addition, subtraction, multiplication, or division.
• They may also include mathematical concepts such as the absolute value or exponents.

For instance, when given integers \(x=2\) and \(y=-5\), substituting these into the expression \(|x|+|y|\) sets the stage for the calculation. It's like replacing variables with their actual values, transforming the expression into something more actionable.

Substitution Method

The substitution method is a fundamental technique used to make algebraic evaluations more straightforward. The main idea is to replace each variable in an expression with given numerical values. This method is particularly helpful when you are dealing with expressions that have more than one variable.

• Identify which variable is being replaced by which number.
• Remove the variable and insert the determined number directly into the expression.

In our exercise, we replaced \(x\) with 2 and \(y\) with -5 in the expression \(|x|+|y|\). This step set us up to evaluate actual numbers rather than abstract variables.
This approach simplifies the process and allows us to accurately calculate the expression's value.

Basic Arithmetic Operations

Once variables have been substituted with specific numbers, performing basic arithmetic operations is the next step. These are the simple math operations we frequently use: addition, subtraction, multiplication, and division.

• Addition: Sum two or more numbers.
• Subtraction: Find the difference between numbers.
• Multiplication: Calculate the product of quantities.
• Division: Determine how many times one number is contained within another.

For an expression like \(|x|+|y|\), once you evaluate the absolute values, you combine them using addition. Here, we found that \(2 + 5 = 7\). Understanding basic arithmetic is crucial because these operations form the backbone of more complex algebraic calculations.