Problem 74 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(3 m\) when \(m=7\)

Step-by-Step Solution

Answer

The evaluated expression is 21.

Step 1: Identify the given variable and its value

The variable is \(m\) and its given value is 7.

Step 2: Substitute the value of the variable into the expression

Substitute \(m\) with 7 in the expression \(3 m\). This gives \(3 * 7\).

Step 3: Simplify the Expression

Multiplying 3 by 7, you get 21.

Key Concepts

Variable Substitution

In algebra, an important step when solving expressions is understanding and applying **variable substitution**. Variables are symbols used to represent unknown values or quantities. They allow us to write expressions that can change based on the value of the variable. For instance, in the expression \(3m\), the variable is \(m\).
Once a specific value is assigned to the variable, we replace the variable with that number in the expression. In our example, when \(m = 7\), substitute the \(m\) with 7, transforming \(3m\) into \(3 \times 7\).
This is the foundational step to solving algebraic expressions involving variables, paving the way for further evaluation.

Evaluation of Expressions

**Evaluation of expressions** involves calculating the numerical value of an expression after variable substitution has been completed. Once we substitute the variable with its given value, all we need to do is perform the arithmetic operations.
In the context of the expression \(3m\) with \(m=7\), after substitution, the expression becomes \(3 \times 7\). Now, our task is to evaluate this. This means to solve it, performing the multiplication operation, to find what the expression equals numerically.
The ability to accurately substitute and evaluate expressions allows us to solve complex algebraic equations by breaking them down into simpler, more manageable steps.

Arithmetic Operations

After substitution and recognizing the expression's structure, we move on to **arithmetic operations**. These are basic mathematical operations, such as addition, subtraction, multiplication, and division.
The operation in our example is multiplication. We have the expression \(3 \times 7\), where multiplication must be used to determine the final result. Here, it involves simply multiplying 3 and 7, resulting in 21.
Understanding arithmetic operations is crucial as these operations are not only foundational for algebra but also for handling more complex mathematical problems.