Combine Like Terms And Simplify:$\[ 15 = X \div 6 \\]

Introduction

In mathematics, combining like terms is a fundamental concept that helps simplify equations and make them easier to solve. Like terms are expressions that have the same variable raised to the same power. In this article, we will explore how to combine like terms and simplify equations using the given example: $15 = x \div 6$.

Understanding Like Terms

Like terms are expressions that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. On the other hand, $2x$ and $3y$ are not like terms because they have different variables.

Combining Like Terms

To combine like terms, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Given Equation

Let's simplify the given equation: $15 = x \div 6$. To do this, we need to combine like terms and isolate the variable $x$.

Step 1: Multiply Both Sides by 6

To get rid of the division, we can multiply both sides of the equation by 6:

$$6 \times 15 = 6 \times (x \div 6)$$

This simplifies to:

$$90 = x$$

Step 2: Check the Solution

To check our solution, we can plug it back into the original equation:

$$15 = x \div 6$$

Substituting $x = 90$, we get:

$$15 = 90 \div 6$$

This simplifies to:

$$15 = 15$$

Which is true!

Conclusion

In this article, we learned how to combine like terms and simplify equations using the given example: $15 = x \div 6$. We followed the order of operations (PEMDAS) and multiplied both sides of the equation by 6 to get rid of the division. We then checked our solution by plugging it back into the original equation. By combining like terms and simplifying equations, we can make math problems easier to solve and understand.

Examples of Combining Like Terms

Here are some examples of combining like terms:

• $2x + 3x = 5x$
• $4y - 2y = 2y$
• $x^2 + 2x^2 = 3x^2$

Tips and Tricks

Here are some tips and tricks for combining like terms:

• Make sure to follow the order of operations (PEMDAS).
• Identify like terms by looking for the same variable raised to the same power.
• Combine like terms by adding or subtracting their coefficients.
• Check your solution by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when combining like terms:

• Forgetting to follow the order of operations (PEMDAS).
• Not identifying like terms correctly.
• Not combining like terms correctly.
• Not checking the solution.

Real-World Applications

Combining like terms has many real-world applications, such as:

• Simplifying algebraic expressions in physics and engineering.
• Solving systems of equations in economics and finance.
• Modeling population growth and decay in biology and ecology.

Conclusion

Introduction

In our previous article, we explored the concept of combining like terms and simplifying equations. In this article, we will answer some frequently asked questions about combining like terms and provide additional examples and tips.

Q&A

Q: What are like terms?

A: Like terms are expressions that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I identify like terms?

A: To identify like terms, look for the same variable raised to the same power. For example, $2x^2$ and $3x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, $2x + 3x = 5x$.

Q: What is the order of operations for combining like terms?

A: The order of operations for combining like terms is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I combine like terms with different variables?

A: No, you cannot combine like terms with different variables. For example, $2x$ and $3y$ are not like terms because they have different variables.

Q: How do I check my solution?

A: To check your solution, plug it back into the original equation. If the solution is true, then you have correctly combined like terms.

Examples

Here are some examples of combining like terms:

• $2x + 3x = 5x$
• $4y - 2y = 2y$
• $x^2 + 2x^2 = 3x^2$
• $3x^2 - 2x^2 = x^2$

Tips and Tricks

Here are some tips and tricks for combining like terms:

• Make sure to follow the order of operations (PEMDAS).
• Identify like terms by looking for the same variable raised to the same power.
• Combine like terms by adding or subtracting their coefficients.
• Check your solution by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when combining like terms:

• Forgetting to follow the order of operations (PEMDAS).
• Not identifying like terms correctly.
• Not combining like terms correctly.
• Not checking the solution.

Real-World Applications

Combining like terms has many real-world applications, such as:

• Simplifying algebraic expressions in physics and engineering.
• Solving systems of equations in economics and finance.
• Modeling population growth and decay in biology and ecology.

Conclusion

In conclusion, combining like terms is a fundamental concept in mathematics that helps simplify equations and make them easier to solve. By following the order of operations (PEMDAS) and identifying like terms, we can combine them and simplify equations. With practice and patience, we can become proficient in combining like terms and solving math problems with ease.

Additional Resources

For more information on combining like terms, check out the following resources:

• Khan Academy: Combining Like Terms
• Mathway: Combining Like Terms
• Wolfram Alpha: Combining Like Terms

Practice Problems

Here are some practice problems to help you master combining like terms:

• Combine the like terms: $2x + 3x + 4x$
• Combine the like terms: $x^2 + 2x^2 + 3x^2$
• Combine the like terms: $4y - 2y + 3y$

Answer Key

Here are the answers to the practice problems:

• $2x + 3x + 4x = 9x$
• $x^2 + 2x^2 + 3x^2 = 6x^2$
• $4y - 2y + 3y = 5y$