Problem 83 - Algebra 2

Question

Evaluate each expression for the given values of the variable. \(6-j ; j=1,2,3,4\)

Step-by-Step Solution

Answer

The results are 5, 4, 3, and 2 for \(j=1, 2, 3,\) and \(4\), respectively.

Step 1: Substitute and Evaluate for j=1

The expression given is \(6-j\). We start by substituting \(j=1\) into the expression. So, it becomes \(6-1\). Calculate the result: \(6-1 = 5\).

Step 2: Substitute and Evaluate for j=2

Next, substitute \(j=2\) into the expression. The expression becomes \(6-2\). Calculate the result: \(6-2 = 4\).

Step 3: Substitute and Evaluate for j=3

Now, substitute \(j=3\) into the expression. The expression becomes \(6-3\). Calculate the result: \(6-3 = 3\).

Step 4: Substitute and Evaluate for j=4

Finally, substitute \(j=4\) into the expression. The expression becomes \(6-4\). Calculate the result: \(6-4 = 2\).

Key Concepts

Evaluation of Expressions

Evaluating expressions is an essential skill in mathematics. It involves calculating the value of an expression by assigning specific values to its variables. In our example, the expression is given as \(6 - j\), and we need to replace \(j\) with specific numbers provided, namely \(1, 2, 3,\) and \(4\).

The goal here is to determine the numerical result for each value of \(j\). Let's consider why this process is beneficial:

• It helps in understanding patterns and relationships within different values.
• It's foundational for solving equations that involve more complex expressions.
• It aids in enhancing mental arithmetic and mathematical accuracy.

When you perform these calculations, you are essentially simplifying the expression by getting rid of the unknowns and replacing them with known quantities. This gives a clear, definite value.

Step by Step Solution

Breaking down problems into smaller steps can significantly enhance understanding. Here's how you can approach the original exercise with clarity:

1. **Identify** the expression and recognize the variable(s). 2. **Substitute** each given value into the expression.3. **Calculate** the result after substitution to find a numerical answer.
First, we take the expression \(6-j\) and substitute \(j=1\). Thus, it becomes \(6-1=5\). Next, substitute \(j=2\), making it \(6-2=4\). Then, when \(j=3\), it becomes \(6-3=3\). Finally, substitute \(j=4\), which is \(6-4=2\).

These calculations demonstrate how breaking the problem down can simplify the process and lead to a quick solution. Each step is clear and involves a simple arithmetic operation, making it easy to follow.

Variable Substitution

The core technique used in this exercise is variable substitution. This involves replacing variables in an expression with particular given numbers. Here, the variable \(j\) takes on different values as specified.

Substitution is essential when you need to evaluate an expression under particular conditions or inputs. It allows for flexibility and adaptability, letting you explore how various inputs affect the overall expression.

• First, ensure you understand what each variable represents.
• Then, confidently replace them with the provided numbers.
• Finally, simplify the expression to reach the answer.

In our scenario, replacing \(j\) with \(1, 2, 3,\) and \(4\) shows the practical application of substitution. This helps direct our focus from abstract variables to concrete numbers, making the math more tangible and understandable.