Simplify The Expression: (3k - 8) + (7k + 12)
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Introduction
In algebra, simplifying expressions is a crucial skill that helps in solving equations and inequalities. It involves combining like terms and eliminating any unnecessary components. In this article, we will focus on simplifying the expression (3k - 8) + (7k + 12), where k is a variable. We will break down the steps involved in simplifying this expression and provide a clear explanation of each step.
Understanding the Expression
The given expression is a combination of two terms: (3k - 8) and (7k + 12). To simplify this expression, we need to combine like terms, which are terms that have the same variable raised to the same power. In this case, the like terms are 3k and 7k.
Like Terms
Like terms are terms that have the same variable raised to the same power. In the given expression, the like terms are 3k and 7k. These terms can be combined by adding or subtracting their coefficients.
Combining Like Terms
To combine like terms, we need to add or subtract their coefficients. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficients of the like terms are 3 and 7.
Adding Coefficients
When adding coefficients, we simply add the numbers together. In this case, we add 3 and 7 to get 10.
Simplifying the Expression
Now that we have combined the like terms, we can simplify the expression by adding the constants. The constants are the numbers that are not multiplied by the variable. In this case, the constants are -8 and 12.
Adding Constants
When adding constants, we simply add the numbers together. In this case, we add -8 and 12 to get 4.
Final Simplified Expression
Now that we have combined the like terms and added the constants, we can write the final simplified expression.
Final Expression
The final simplified expression is 10k + 4.
Conclusion
Simplifying expressions is an essential skill in algebra that helps in solving equations and inequalities. By combining like terms and eliminating unnecessary components, we can simplify complex expressions and make them easier to work with. In this article, we simplified the expression (3k - 8) + (7k + 12) by combining like terms and adding constants. The final simplified expression is 10k + 4.
Example Problems
Problem 1
Simplify the expression (2x - 5) + (4x + 3).
Solution
To simplify this expression, we need to combine like terms. The like terms are 2x and 4x. We can combine these terms by adding their coefficients.
2x + 4x = 6x
Now that we have combined the like terms, we can simplify the expression by adding the constants.
-5 + 3 = -2
The final simplified expression is 6x - 2.
Problem 2
Simplify the expression (3y + 2) + (2y -5).
Solution
To simplify this expression, we need to combine like terms. The like terms are 3y and 2y. We can combine these terms by adding their coefficients.
3y + 2y = 5y
Now that we have combined the like terms, we can simplify the expression by adding the constants.
2 - 5 = -3
The final simplified expression is 5y - 3.
Tips and Tricks
Tip 1
When simplifying expressions, make sure to combine like terms first. This will help you eliminate unnecessary components and make the expression easier to work with.
Tip 2
When adding coefficients, make sure to add the numbers together. This will help you get the correct result.
Tip 3
When adding constants, make sure to add the numbers together. This will help you get the correct result.
Common Mistakes
Mistake 1
Not combining like terms first. This can lead to incorrect results and make the expression more difficult to work with.
Mistake 2
Not adding coefficients correctly. This can lead to incorrect results and make the expression more difficult to work with.
Mistake 3
Not adding constants correctly. This can lead to incorrect results and make the expression more difficult to work with.
Final Thoughts
Simplifying expressions is an essential skill in algebra that helps in solving equations and inequalities. By combining like terms and eliminating unnecessary components, we can simplify complex expressions and make them easier to work with. In this article, we simplified the expression (3k - 8) + (7k + 12) by combining like terms and adding constants. The final simplified expression is 10k + 4. We also provided example problems and tips and tricks to help you simplify expressions like a pro.
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Introduction
In our previous article, we simplified the expression (3k - 8) + (7k + 12) by combining like terms and adding constants. We also provided example problems and tips and tricks to help you simplify expressions like a pro. In this article, we will answer some frequently asked questions about simplifying expressions.
Q&A
Q1: What are like terms?
A1: Like terms are terms that have the same variable raised to the same power. In the expression (3k - 8) + (7k + 12), the like terms are 3k and 7k.
Q2: How do I combine like terms?
A2: To combine like terms, you need to add or subtract their coefficients. The coefficient of a term is the number that is multiplied by the variable. In the expression (3k - 8) + (7k + 12), the coefficients of the like terms are 3 and 7.
Q3: What is the difference between combining like terms and adding constants?
A3: Combining like terms involves adding or subtracting the coefficients of the like terms, while adding constants involves adding the numbers that are not multiplied by the variable.
Q4: How do I add constants?
A4: To add constants, you simply add the numbers together. In the expression (3k - 8) + (7k + 12), the constants are -8 and 12.
Q5: What is the final simplified expression for (3k - 8) + (7k + 12)?
A5: The final simplified expression for (3k - 8) + (7k + 12) is 10k + 4.
Q6: Can I simplify expressions with variables in the denominator?
A6: Yes, you can simplify expressions with variables in the denominator. However, you need to follow the rules of algebra and simplify the expression carefully.
Q7: How do I simplify expressions with fractions?
A7: To simplify expressions with fractions, you need to follow the rules of algebra and simplify the expression carefully. You can start by simplifying the numerator and denominator separately.
Q8: Can I simplify expressions with exponents?
A8: Yes, you can simplify expressions with exponents. However, you need to follow the rules of algebra and simplify the expression carefully.
Q9: How do I simplify expressions with absolute values?
A9: To simplify expressions with absolute values, you need to follow the rules of algebra and simplify the expression carefully. You can start by simplifying the expression inside the absolute value.
Q10: Can I simplify expressions with radicals?
A10: Yes, you can simplify expressions with radicals. However, you need to follow the rules of algebra and simplify the expression carefully.
Conclusion
Simplifying expressions is an essential skill in algebra that helps in solving equations and inequalities. By combining like terms and eliminating unnecessary components, we can simplify complex expressions and make them easier to work with. this article, we answered some frequently asked questions about simplifying expressions and provided tips and tricks to help you simplify expressions like a pro.
Example Problems
Problem 1
Simplify the expression (2x - 5) + (4x + 3).
Solution
To simplify this expression, we need to combine like terms. The like terms are 2x and 4x. We can combine these terms by adding their coefficients.
2x + 4x = 6x
Now that we have combined the like terms, we can simplify the expression by adding the constants.
-5 + 3 = -2
The final simplified expression is 6x - 2.
Problem 2
Simplify the expression (3y + 2) + (2y -5).
Solution
To simplify this expression, we need to combine like terms. The like terms are 3y and 2y. We can combine these terms by adding their coefficients.
3y + 2y = 5y
Now that we have combined the like terms, we can simplify the expression by adding the constants.
2 - 5 = -3
The final simplified expression is 5y - 3.
Tips and Tricks
Tip 1
When simplifying expressions, make sure to combine like terms first. This will help you eliminate unnecessary components and make the expression easier to work with.
Tip 2
When adding coefficients, make sure to add the numbers together. This will help you get the correct result.
Tip 3
When adding constants, make sure to add the numbers together. This will help you get the correct result.
Common Mistakes
Mistake 1
Not combining like terms first. This can lead to incorrect results and make the expression more difficult to work with.
Mistake 2
Not adding coefficients correctly. This can lead to incorrect results and make the expression more difficult to work with.
Mistake 3
Not adding constants correctly. This can lead to incorrect results and make the expression more difficult to work with.
Final Thoughts
Simplifying expressions is an essential skill in algebra that helps in solving equations and inequalities. By combining like terms and eliminating unnecessary components, we can simplify complex expressions and make them easier to work with. In this article, we answered some frequently asked questions about simplifying expressions and provided tips and tricks to help you simplify expressions like a pro.