Problem 64 - Algebra 1: Concepts and Skills

Question

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable. (Lesson 1.1) \(b-12\) when \(b=43\)

Step-by-Step Solution

Answer

Hence, the evaluated expression for \(b-12\) when \(b=43\), is \(31\).

Step 1: Substitute the given value

Begin by substituting \(b\) with \(43\) in the given expression. It becomes \(43 - 12\).

Step 2: Perform the subtraction

Then, execute the subtraction operation. That gives \(31\).

Key Concepts

Substitution Method in Algebra

The substitution method is a fundamental component of algebra that comes into play when we're dealing with variables and expressions. It's like swapping out a placeholder with its actual value. In classroom exercises like the one provided, you'll encounter problems where you're given an expression and a specific value for a variable.

In the case of our example, you had the expression \( b - 12 \) and you were told that \( b = 43 \). The substitution here is straightforward: wherever you see the variable \( b \), you replace it with the number 43. This is step one because before we can solve the expression, we need to know exactly what numbers we're working with. This method not only simplifies the calculation but also lays the groundwork for understanding more complex algebraic operations that you'll encounter later on.

Simple Arithmetic Operations

Once you have made your substitutions, the next step is to carry out the necessary arithmetic operations. These operations include addition, subtraction, multiplication, and division—the basic building blocks of mathematics. In our exercise, the operation required after substitution was subtraction.

To solve \( 43 - 12 \), you take the value you've substituted for \( b \), which is 43, and subtract 12 from it. Subtraction essentially means taking away a certain amount from a larger quantity. The result, in this case, is \( 31 \). It's crucial to be comfortable with these operations because they're not only used in algebra but in nearly every aspect of math. Practice often, and if needed, you can use a calculator or number line to help you understand these operations better.

Algebraic Expressions

Algebraic expressions are a mix of numbers, variables (like \( b \)), and operation signs (such as '+', '-', '*', '/'). The expression \( b - 12 \) is a simple example of an algebraic expression. Despite its simplicity, understanding expressions is key to mastering algebra. They can represent real-world quantities and scenarios, giving us a powerful language for describing mathematical problems.

When an expression contains a variable, as in our exercise, you cannot fully solve it until you are given a specific value for that variable. Without the value of \( b \), the expression \( b - 12 \) could represent any number of things. But by knowing \( b = 43 \), we can evaluate the expression and find a single numerical answer. As you progress in algebra, you'll learn to manipulate these expressions in more sophisticated ways, but it all starts with the basic understanding of substituting and simplifying as we've done here.