Problem 15 - Elementary and Intermediate Algebra

Question

The Try Exercises for examples are indicated by a shaded block on the exercise number. Answers to these exercises appear at the end of the exercise set as well as at the back of the book. $$ t+6, \text { for } t=2 $$

Step-by-Step Solution

Answer

8

Step 1: Identify the Given Expression and Variable

The given expression is \( t + 6 \). The value of the variable t is specified as 2.

Step 2: Substitute the Variable

Replace the variable \( t \) with the given value 2 in the expression \( t + 6 \). This results in \( 2 + 6 \).

Step 3: Perform the Calculation

Calculate the result of the expression \( 2 + 6 \). This equals 8.

Key Concepts

Algebraic expressions

In algebra, an expression is a combination of numbers, variables, and operations. Algebraic expressions do not contain an equal sign, which differentiates them from equations. For example, the expression in our exercise is \(t + 6\).

Here, \(t\) is a variable, and 6 is a constant. The plus sign (+) is an operation indicating addition.

Understanding how to manipulate and evaluate algebraic expressions is fundamental to mastering algebra. It allows you to form equations and solve mathematical problems efficiently.

Variable substitution

Variable substitution is a method used to simplify algebraic expressions by replacing the variable with a given value.
This method is useful for evaluating expressions and solving equations. Here's how it works:

Let's take our example from the exercise: \(t + 6\). You are given a specific value for the variable \(t\), which is 2. Substituting the variable means you replace every instance of \(t\) in the expression with the given value.

So, \(t + 6\) becomes \(2 + 6\) after substitution.
This process helps in understanding the expression by converting it into a simpler arithmetic problem.

Basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. In our exercise, we are dealing with addition.

After substituting the variable \(t\) with 2 in the expression \(t + 6\), we get \(2 + 6\). To solve this, we simply perform the addition operation:

• Add the numbers together: 2 + 6
• The result is 8

This step-by-step approach ensures you understand the process, making it easier to handle more complex problems in the future.

Remember, mastering basic arithmetic is key to succeeding in algebra and other higher-level math topics.