3z 5m - 3 4m - 2z

Simplifying Algebraic Expressions: Solving 3z + 5m - 3 - 4m - 2z

This article will guide you through simplifying the algebraic expression 3z + 5m - 3 - 4m - 2z. We'll break down the process step-by-step, explaining the underlying principles of algebra and providing a clear, concise solution. Understanding how to simplify expressions like this is fundamental to success in algebra and beyond. This is a great example of combining like terms, a key concept in algebraic manipulation.

Understanding Like Terms

Before we begin, let's define what "like terms" are. Like terms are terms that have the same variables raised to the same powers. For example, 3z and -2z are like terms because they both have the variable 'z' raised to the power of 1. Similarly, 5m and -4m are like terms because they both have the variable 'm' raised to the power of 1. The constant term, -3, stands alone as it doesn't contain any variables.

Step-by-Step Simplification

1. Identify Like Terms: The first step is to identify the like terms in the expression 3z + 5m - 3 - 4m - 2z. We have:

   • z terms: 3z and -2z
   • m terms: 5m and -4m
   • constant term: -3

2. Combine Like Terms: Now, we combine the like terms by adding or subtracting their coefficients (the numbers in front of the variables).

   • z terms: 3z + (-2z) = (3 - 2)z = 1z = z
   • m terms: 5m + (-4m) = (5 - 4)m = 1m = m

3. Rewrite the Simplified Expression: After combining the like terms, the simplified expression becomes:

   z + m - 3

Final Answer and Conclusion

Therefore, the simplified form of the algebraic expression 3z + 5m - 3 - 4m - 2z is z + m - 3. This process demonstrates the fundamental principle of combining like terms in algebra. Mastering this skill is crucial for tackling more complex algebraic equations and problem-solving. Remember to always carefully identify like terms before combining them to avoid errors. Practice simplifying different algebraic expressions to further build your understanding and proficiency. This will improve your overall algebraic skills and prepare you for more advanced mathematical concepts.