Problem 16 - 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. $$ 13-r, \text { for } r=9 $$

Step-by-Step Solution

Answer

4

Step 1: Understand the Expression

The given expression is 13 - r, and we need to find its value for r = 9.

Step 2: Substitute the Value

Substitute the value of r with 9 in the expression. This gives us: 13 - 9.

Step 3: Simplify the Expression

Perform the subtraction: 13 - 9 = 4.

Step 4: State the Result

Therefore, the value of the expression 13 - r for r = 9 is 4.

Key Concepts

substitution method

Solving algebraic expressions often involves using the substitution method. This is a technique where you replace a variable with a given number. The goal is to make the expression easier to evaluate. Let's look at the provided exercise. The expression is 13 - r, and we need to find its value when r = 9.
Steps to use the substitution method:

• Identify the variable in the expression. Here, it is 'r'.
• Replace 'r' with the given value, which is 9. This changes the expression to 13 - 9.
• Now, the expression without the variable is easier to solve.

Using substitution makes it clear and straightforward to find the desired value.

simplification

After substituting the value in the expression, the next step is simplification. Simplifying means performing basic arithmetic operations to get the final result. In our exercise, once we substitute 'r' with 9, we get 13 - 9.
Steps to simplify:

• Look for arithmetic operations that need to be performed.
• In this case, it's a subtraction: 13 - 9.
• Perform the subtraction. Here, you subtract 9 from 13 to get 4.

Simplification is crucial because it leads us step-by-step to the simplest form of the expression. It converts a potentially complex expression into a more manageable result.

basic arithmetic

Basic arithmetic is the foundation of solving algebraic expressions. It involves basic operations like addition, subtraction, multiplication, and division. In our exercise, we focused on subtraction:
Subtraction:
The problem 13 - 9 illustrates the importance of understanding basic subtraction. Subtraction means taking away one quantity from another. To subtract 9 from 13:

• Start from the number 13.
• Count down 9 steps, or visualize removing 9 items from a group of 13.
• The count stops at 4.

Knowing basic arithmetic helps simplify algebraic expressions, making problems easier to solve and understand. It is the skill that underpins more complex math concepts.