Simplifying Expressions: A Step-by-Step Guide
Mathematics often involves working with expressions containing variables and numbers. Simplifying these expressions makes them easier to understand and work with. Let's take a look at how to simplify the expression 9k - 5 + k + 3.
1. Identify Like Terms:
First, we need to identify the terms that have the same variable and exponent. In this case, our like terms are 9k and k.
2. Combine Like Terms:
We can combine the 9k and k by adding their coefficients (the numbers in front of the variables). This gives us 10k.
3. Combine Constant Terms:
Next, we combine the constant terms, which are the numbers without variables. In this case, we have -5 and 3. Adding these together gives us -2.
4. Final Simplified Expression:
After combining like terms and constant terms, we arrive at the simplified expression: 10k - 2.
Example:
Let's say k = 2. We can substitute this value into our simplified expression:
10(2) - 2
Simplifying this gives us:
20 - 2 = 18
Tips for Simplifying Expressions:
- Always follow the order of operations (PEMDAS/BODMAS)
- Identify like terms carefully.
- Combine like terms by adding or subtracting their coefficients.
- Simplify constant terms separately.
Conclusion:
Simplifying expressions is an important skill in mathematics. By combining like terms and constant terms, we can express the same information in a more concise and understandable form. This process is especially helpful when solving equations and working with more complex expressions.