Problem 50 - Algebra A Combined Function

Question

Evaluate each expression when \(x=1, y=3,\) and \(z=5 .\) \(4 x\)

Step-by-Step Solution

Answer

4

Step 1: Identify the expression

The expression given is \(4x\). Our task is to evaluate this expression using the provided values for \(x\), \(y\), and \(z\).

Step 2: Substitute the value of \(x\)

The value given for \(x\) is 1. Substitute this value into the expression: \(4 \cdot 1\).

Step 3: Perform the multiplication

Now multiply the values: \(4 \cdot 1 = 4\).

Key Concepts

Substitution Method

The substitution method is a fundamental concept in algebra that involves replacing variables with their given numerical values. In this exercise, we're given the expression \(4x\) and need to evaluate it for specific values of \(x\), \(y\), and \(z\). When using this method, the key steps include:

• Identify the variable in the expression — here, it's \(x\).
• Find the given numerical value for this variable — in our case, \(x = 1\).
• Replace the variable in the expression with its numerical value. So, \(4x\) becomes \(4 \cdot 1\).

Applying the substitution method allows us to convert algebraic expressions into arithmetic operations that can be easily calculated. This method is crucial for solving equations in algebra by simplifying terms using known values.

Basic Algebra

Basic algebra involves working with symbols and letters to stand in for numbers. It's the foundation for solving mathematical problems and understanding complex equations. Here's what you need to know about basic algebra principles:

• Variables: Letters like \(x\), \(y\), and \(z\) are used to represent unknown values or values that can change. In our exercise, \(x = 1\), \(y = 3\), and \(z = 5\).
• Expressions: A combination of numbers, variables, and operations. The expression \(4x\) involves multiplication of a number with a variable.
• Operations: Basic algebra includes addition, subtraction, multiplication, and division. In this case, multiplication is the operation used in \(4x\).

Understanding these principles helps in evaluating expressions and solving equations, laying the groundwork for more advanced algebraic concepts.

Multiplication in Algebra

Multiplication in algebra is similar to multiplication of numbers but involves variables. It is an operation that combines numbers or variables in an expression. Here's how it works with our example:The expression \(4x\) signifies multiplication between \(4\) (a constant) and \(x\) (a variable). To evaluate it, follow these steps:

• Substitute the value of the variable. For \(x = 1\), replace \(x\) in \(4x\) with \(1\).
• Perform the multiplication: \(4 \cdot 1\).
• Calculate the result, which equals \(4\).

This straightforward process shows how multiplication in algebra simplifies once variables are substituted by their numerical values. Understanding this helps in solving more complex algebraic expressions that involve multiple operations and variables.