Write An Expression Equivalent To$\[1.3x + 4.2x - 2.4x - 5.7x\\]
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In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable raised to the same power. In this article, we will explore how to simplify the given expression by combining like terms.
Understanding the Expression
The given expression is:
This expression consists of four terms, each with the variable x. To simplify this expression, we need to combine the like terms.
Identifying Like Terms
Like terms are terms that have the same variable raised to the same power. In this expression, the like terms are the terms with the variable x. We can identify the like terms by looking at the coefficients of x.
The coefficients of x in the given expression are:
- 1.3
- 4.2
- -2.4
- -5.7
Combining Like Terms
To combine like terms, we need to add or subtract the coefficients of the like terms. In this case, we can combine the terms with the variable x by adding or subtracting their coefficients.
Evaluating the Expression
Now, we can evaluate the expression by adding or subtracting the coefficients of the like terms.
Therefore, the simplified expression is:
Conclusion
In this article, we learned how to simplify the given expression by combining like terms. We identified the like terms, combined them by adding or subtracting their coefficients, and evaluated the expression to get the simplified result. This process is essential in algebra, as it helps simplify complex expressions and makes it easier to solve equations and inequalities.
Real-World Applications
Combining like terms has many real-world applications in various fields, such as:
- Physics: When solving problems involving motion, combining like terms helps simplify the equations and make it easier to calculate the position, velocity, and acceleration of an object.
- Engineering: In engineering, combining like terms is used to simplify complex equations and make it easier to design and analyze systems.
- Computer Science: In computer science, combining like terms is used to simplify complex algorithms and make it easier to write efficient code.
Tips and Tricks
Here are some tips and tricks to help you simplify expressions by combining like terms:
- Identify the like terms: Look for terms with the same variable raised to the same power.
- Combine the coefficients: Add or subtract the coefficients of the like terms.
- Evaluate the expression: Simplify the expression by combining the like terms.
By following these tips and tricks, you can simplify complex expressions and make it easier to solve equations and inequalities.
Common Mistakes
Here are some common mistakes to avoid when simplifying expressions by combining like terms:
- Not identifying the like terms: Failing to identify the like terms can lead to incorrect simplification.
- Not combining the coefficients: Failing to combine the coefficients of the like terms can lead to incorrect simplification.
- Not evaluating the expression: Failing to evaluate the expression can lead to incorrect simplification.
By avoiding these common mistakes, you can simplify complex expressions and make it easier to solve equations and inequalities.
Final Thoughts
In conclusion, combining like terms is a fundamental concept in algebra that helps simplify complex expressions. By identifying the like terms, combining their coefficients, and evaluating the expression, you can simplify complex expressions and make it easier to solve equations and inequalities. Remember to follow the tips and tricks, and avoid the common mistakes to ensure accurate simplification.
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In our previous article, we explored how to simplify algebraic expressions by combining like terms. In this article, we will answer some frequently asked questions about combining like terms.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. In other words, they have the same base and exponent.
Q: How do I identify like terms?
A: To identify like terms, look for terms with the same variable raised to the same power. For example, in the expression 2x + 3x - 4x, the like terms are 2x, 3x, and -4x because they all have the variable x raised to the power of 1.
Q: Can I combine terms with different variables?
A: No, you cannot combine terms with different variables. For example, in the expression 2x + 3y - 4x, you cannot combine the terms 2x and 3y because they have different variables.
Q: Can I combine terms with different exponents?
A: No, you cannot combine terms with different exponents. For example, in the expression 2x^2 + 3x - 4x^3, you cannot combine the terms 2x^2 and 3x because they have different exponents.
Q: How do I combine like terms with negative coefficients?
A: When combining like terms with negative coefficients, you need to change the sign of the coefficient when adding or subtracting. For example, in the expression -2x + 3x - 4x, you need to change the sign of the coefficient when adding or subtracting, so the expression becomes -2x + 3x - 4x = -3x.
Q: Can I combine like terms with fractions?
A: Yes, you can combine like terms with fractions. For example, in the expression 1/2x + 3/2x - 4/2x, you can combine the terms by adding or subtracting the numerators and keeping the denominator the same.
Q: How do I simplify expressions with multiple like terms?
A: To simplify expressions with multiple like terms, you need to combine the like terms by adding or subtracting their coefficients. For example, in the expression 2x + 3x - 4x + 5x, you need to combine the like terms by adding or subtracting their coefficients, so the expression becomes 2x + 3x - 4x + 5x = 6x.
Q: Can I use a calculator to simplify expressions with like terms?
A: Yes, you can use a calculator to simplify expressions with like terms. However, it's always a good idea to check your work by hand to make sure you get the correct answer.
Q: What are some common mistakes to avoid when combining like terms?
A: Some common mistakes to avoid when combining like terms include:
- Not identifying the like terms
- Not combining the coefficients of the like terms
- Not evaluating the expression
- Combining terms with different variables or exponents
By avoiding these common mistakes, you can ensure accurate simplification of expressions with like terms.
Q: How can I practice combining like terms?
A: You can practice combining like terms by working through examples and exercises in your textbook or online resources. You can also try creating your own examples and simplifying them to practice your skills.
Q: What are some real-world applications of combining like terms?
A: Combining like terms has many real-world applications in various fields, such as:
- Physics: When solving problems involving motion, combining like terms helps simplify the equations and make it easier to calculate the position, velocity, and acceleration of an object.
- Engineering: In engineering, combining like terms is used to simplify complex equations and make it easier to design and analyze systems.
- Computer Science: In computer science, combining like terms is used to simplify complex algorithms and make it easier to write efficient code.
By understanding how to combine like terms, you can simplify complex expressions and make it easier to solve equations and inequalities in various fields.