Problem 60 - Algebra 1

Question

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 8 b+5-3 b $$

Step-by-Step Solution

Answer

The simplified expression is \(5 b + 5\).

Step 1: Identify the Like Terms

In the given expression \(8 b+5-3 b\), the like terms are \(8 b\) and \(-3 b\). They have been identified as like terms because both contain the variable 'b' with the power of 1.

Step 2: Combine the Like Terms

When we combine the like terms together, we add or subtract their coefficients while keeping the variable unchanged. So, \(8 b - 3 b = 5 b\)

Step 3: Write the Final Expression

After combining the like terms, you write down the final simplified expression. So, the 5 from the beginning of the equation remains and the simplified expression is \(5 b + 5\).

Key Concepts

Combining Like Terms

When simplifying algebraic expressions, one of the core skills you need to master is combining like terms. But what exactly are "like terms"? Simply put, like terms are terms within an algebraic expression that have the same variables raised to the same powers. For example, in the expression \(8b + 5 - 3b\), the terms \(8b\) and \(-3b\) are like because they both involve the variable \(b\) raised to the power of 1.

To combine like terms, you focus on the coefficients, which are the numbers in front of the variables. In our expression, the coefficients are 8 and -3. Adding these coefficients together gives us:

• \(8 + (-3) = 5\).

So, combining \(8b\) and \(-3b\) gives us \(5b\), leaving us with the simplified expression \(5b + 5\). This process streamlines the expression by reducing the number of terms, making calculations easier!

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. In the exercise above, \(8b + 5 - 3b\) is an algebraic expression that contains numbers, a variable \(b\), and subtraction and addition operations.

These expressions can represent real-world situations or abstract mathematical ideas. Understanding how to work with them, especially how to simplify them by combining like terms, is key in algebra.

• Variables like \(b\) can represent unknown numbers.
• Expressions don't include equality signs—that's the job of equations.
• Simplification makes expressions easier to work with and understand.

By mastering algebraic expressions, you lay the foundation for solving equations and many other math concepts.

Basic Algebra

Basic algebra is the stepping stone into the world of more advanced mathematics. It primarily involves working with numbers and letters that represent numbers through a series of arithmetic operations. The fundamental skills you learn in basic algebra include simplifying expressions, solving equations, and understanding functions.

When it comes to simplifying expressions like \(8b + 5 - 3b\), the goal is to make computations easier and expressions clearer. This involves identifying like terms to reduce the expression as shown in our example.

• Algebra equips you with tools to solve real-world problems.
• It helps develop logical thinking and reasoning skills.
• Understanding basic algebra is essential for progressing to higher math levels.

With practice, basic algebra becomes a simple yet powerful tool for solving everyday problems.