The problem asks us to combine two algebraic expressions, 6x + 5 and -3x - 4, and simplify the result. This involves applying the principles of combining like terms....
Combining Like Terms
Like terms are those that have the same variable and exponent. In our expressions, we have:
- 6x and -3x are like terms (both have 'x' to the power 1).
- 5 and -4 are like terms (both are constant terms).
Steps to Simplify the Expression
Let's break down the process step-by-step:
- Identify the like terms: In 6x + 5 and -3x - 4, we have identified the like terms.
- Combine the coefficients of the like terms: The coefficients are the numbers multiplying the variables. So, for the 'x' terms, we have 6 - 3 = 3. For the constant terms, we have 5 - 4 = 1.
- Write the simplified expression: Combining the results from step 2, the simplified expression becomes 3x + 1.
The Solution
Therefore, the sum of 6x + 5 and -3x - 4 in its simplest form is 3x + 1.
Visual Representation
Let's visualize this process:
6x + 5
-3x - 4
-------
3x + 1
Key Concepts
This problem demonstrates the fundamental concept of combining like terms in algebra. It also emphasizes the importance of correctly applying the rules of addition and subtraction while working with algebraic expressions.
Practice Problems
To solidify your understanding, try simplifying the following expressions:
- 4y + 2 - 2y - 5
- 7a - 3b + 5a + 2b
- -9m + 4n + 2m - 7n
Conclusion
Simplifying algebraic expressions like 6x + 5 and -3x - 4 is a common practice in algebra. Understanding the concept of like terms and applying the correct operations is crucial for achieving a simplified, accurate result.