Problem 20 - Algebra 1

Question

\(b-7\) when \(b=24\)

Step-by-Step Solution

Answer

The result of the evaluated expression is 17.

Step 1: Identify the variable

In the given algebraic expression \(b-7\), b is the variable.

Step 2: Substitute the variable

Replace the variable b in \(b-7\) with the given value, 24.

Step 3: Evaluate the expression

After substitution the expression becomes \(24-7\). When we subtract 7 from 24, we get 17.

Key Concepts

Variable Substitution

In algebra, variables are symbols that represent numbers. They are like placeholders. In the expression \(b-7\), the letter \(b\) is a variable. It can be replaced by a specific number. This process is called **substitution**. For instance, if given that \(b = 24\), you simply replace every occurrence of \(b\) with 24. This turns the expression from \(b-7\) into \(24-7\). Substitution helps transform algebraic expressions into numerical ones, making them easier to handle and solve.

Evaluating Expressions

Once you have replaced the variable with a number, the next step is to evaluate the expression. Evaluating means performing the arithmetic operations to find the numerical value. Given the expression \(24-7\), you subtract 7 from 24. Performing the calculation:

• Start with 24.
• Subtract 7.
• The result is 17.

Evaluating doesn't only apply to simple operations like subtraction. It can also involve addition, multiplication, division, or combinations of these. Every time you substitute a value into an expression and calculate, you are evaluating it.

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and operators (like +, -, *, /). They can represent a wide range of problems or situations. Unlike pure numbers, expressions with variables can change their value based on the variables' assigned numbers. For instance, in the expression \(b-7\), the outcome changes depending on the value of \(b\). Another example is \(x + 3\), where if \(x = 5\), the expression becomes 8.Algebraic expressions form the basis for creating equations and functions. They allow us to create models for real-world problems, making algebra a powerful mathematical tool. Understanding these expressions is essential in mastering algebra and applying it in solving practical problems.