Problem 75 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(d-13\) when \(d=22\)

Step-by-Step Solution

Answer

The evaluated expression is 9.

Step 1: Identify the variable and its value

From the given exercise, the variable is \(d\) and its value is 22.

Step 2: Substitute the variable's value into the expression

The expression given is \(d-13\). By substituting the value of variable \(d = 22\) into the expression, we rewrite the expression as \(22 - 13\).

Step 3: Solve the Expression

After the substitution, solve the expression. This means to perform the subtraction \(22 - 13\).

Key Concepts

Variable Substitution

Variable substitution in algebra is the process of replacing a variable, often represented by a letter, with a specific number. This step is crucial because it allows us to perform calculations and find concrete results.
This technique is very common in algebraic expressions where you're given a specific value for the variable.

• The first step in variable substitution is to correctly identify the variable and its value. For instance, in our exercise, the variable is \(d\), and its given value is 22.
• Once the variable and its value are understood, the next step is to substitute this value into the expression wherever the variable appears. This changes our expression from a general form to a specific one, which can then be easily evaluated.

By substituting, you are essentially transforming the problem into a simpler, number-focused format, which makes it easier to solve using basic arithmetic.

Evaluating Expressions

Evaluating expressions is about taking the expression with the substituted values and finding the final numerical answer. With the variable replaced by its given number, you perform the indicated arithmetic operations.
Here's how it works:

• Start by ensuring all variables in the expression have been replaced with their assigned values, turning the expression into a numerical one.
• Apply the correct arithmetic operations, such as addition, subtraction, multiplication, or division, as dictated by the expression. In our exercise, after substitution, the expression becomes \(22 - 13\).
• By solving this, you arrive at a final numerical answer. For \(22 - 13\), this would be 9.

Evaluating expressions is a key skill in algebra, as it translates abstract information into actionable numerical solutions.

Basic Algebra Operations

Basic algebra operations are the fundamental arithmetic processes that are used in solving algebraic expressions. These operations include addition, subtraction, multiplication, and division. In our exercise, the main operation used is subtraction.

• Understand the order of operations, commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. This tells us which operations to perform first in a complex expression, although our current example is straightforward.
• In our specific example, since the expression after substitution is \(22 - 13\), we focus only on performing the subtraction, which involves taking away 13 from 22 to get 9.

Mastering these basic operations opens the door to solving more advanced problems in algebra and other fields of mathematics.