Problem 71 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(c+4\) when \(c=24\)

Step-by-Step Solution

Answer

The value of the expression \(c + 4\) when \(c = 24\) is equal to 28.

Step 1: Substitute the value of c

Replace \(c\) in the expression \(c+4\) with the given value 24. This results in the new expression \(24 + 4\).

Step 2: Simplify

Perform the operation to get the value of the expression. Calculate \(24 + 4\) which equals to 28.

Key Concepts

Substitution

Substitution is a fundamental concept in algebra where we replace variables with known values. This concept helps solve equations and evaluate expressions. In our example, to evaluate the expression \(c+4\) when \(c=24\), we apply substitution by swapping the variable \(c\) with its given value, which simplifies our expression to \(24 + 4\).
Here’s why substitution is useful:

• It allows us to transform expressions into numerical calculations that are easier to understand.
• It clears up expressions or equations by filling in numerical values, making it possible to find a specific answer.
• It is a stepping stone towards solving more complex algebraic equations.

Master this skill early because substitution is a building block for more advanced math topics!

Simplification

Once substitution is done, the next step is simplification. Simplification involves reducing an expression to its simplest form, making it easier to interpret and solve. In the context of our exercise, after substituting 24 for \(c\) in \(c+4\), the expression becomes \(24 + 4\). Now, we simplify by performing the basic arithmetic addition.
Simplification is crucial because:

• It allows us to plainly see the result of an expression.
• It reduces complex expressions, providing clarity and reducing the volume of calculations.
• It helps in avoiding errors that might occur from manipulating more complex expressions prematurely.

So whenever faced with algebra problems, always aim to simplify as much as possible!

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. These operations are essential for calculating the results of simplified expressions. For the expression \(24 + 4\), we focus on addition, the most basic arithmetic operation, to determine the value of the expression.
Understanding arithmetic is key because:

• It forms the basis of all mathematical computations.
• Grasping these operations lets you handle more complex math scenarios with confidence.
• Accuracy in arithmetic directly affects the correctness of your final solution.

Practicing these operations will strengthen your mathematical skills and improve problem-solving abilities!