Simplify The Expression:${ -2(-2x - 5) + 3(2x - 9) }$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, removing parentheses, and rearranging the expression to make it easier to work with. In this article, we will simplify the given expression: $-2(-2x - 5) + 3(2x - 9)$. We will break down the steps involved in simplifying the expression and provide a clear explanation of each step.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to the terms inside the parentheses. When we distribute a negative sign, we change the sign of each term inside the parentheses.

-2(-2x - 5) = 4x + 10

Step 2: Distribute the Positive Sign

Next, we distribute the positive sign to the terms inside the parentheses. When we distribute a positive sign, we keep the sign of each term inside the parentheses.

3(2x - 9) = 6x - 27

Step 3: Combine Like Terms

Now that we have distributed the signs, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable x: 4x and 6x.

4x + 6x = 10x

Step 4: Combine Constants

We also have two constant terms: 10 and -27. We can combine these terms by adding them together.

10 - 27 = -17

Step 5: Simplify the Expression

Now that we have combined like terms and constants, we can simplify the expression by combining the results of the previous steps.

10x - 17

Conclusion

In this article, we simplified the given expression: $-2(-2x - 5) + 3(2x - 9)$. We broke down the steps involved in simplifying the expression and provided a clear explanation of each step. By following these steps, we can simplify any expression and make it easier to work with.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions:

• Always distribute the signs to the terms inside the parentheses.
• Combine like terms by adding or subtracting the coefficients of the terms.
• Combine constants by adding or subtracting the constants.
• Simplify the expression by combining the results of the previous steps.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

• Simplify the expression: $-3(2x + 5) + 2(x - 3)$
• Simplify the expression: $4(x - 2) + 3(x + 5)$
• Simplify the expression: $-2(x + 3) + 5(x - 2)$

Real-World Applications

Simplifying expressions has many real-world applications. For example:

• In physics, we use simplifying expressions to solve problems involving motion and energy.
• In engineering, we use simplifying expressions to design and optimize systems.
• In economics, we use simplifying expressions to model and analyze economic systems.

Conclusion

Introduction

In our previous article, we simplified the expression: $-2(-2x - 5) + 3(2x - 9)$. We broke down the steps involved in simplifying the expression and provided a clear explanation of each step. In this article, we will answer some frequently asked questions about simplifying expressions.

Q: What is the first step in simplifying an expression?

A: The first step in simplifying an expression is to distribute the signs to the terms inside the parentheses. When we distribute a negative sign, we change the sign of each term inside the parentheses. When we distribute a positive sign, we keep the sign of each term inside the parentheses.

Q: How do I combine like terms?

A: To combine like terms, we add or subtract the coefficients of the terms. For example, if we have two terms with the variable x: 4x and 6x, we can combine them by adding their coefficients: 4x + 6x = 10x.

Q: What is the difference between combining like terms and combining constants?

A: Combining like terms involves adding or subtracting the coefficients of terms with the same variable raised to the same power. Combining constants involves adding or subtracting the constants.

Q: Can I simplify an expression by rearranging the terms?

A: Yes, you can simplify an expression by rearranging the terms. However, this should be done after you have combined like terms and constants.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms left to combine and no constants left to combine. In other words, the expression should be in its simplest form.

Q: Can I use a calculator to simplify an expression?

A: Yes, you can use a calculator to simplify an expression. However, it's always a good idea to check your work by hand to make sure you understand the steps involved in simplifying the expression.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not distributing the signs to the terms inside the parentheses
• Not combining like terms
• Not combining constants
• Not checking your work by hand

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through practice problems, such as the ones listed below:

• Simplify the expression: $-3(2x + 5) + 2(x - 3)$
• Simplify the expression: $4(x - 2) + 3(x + 5)$
• Simplify the expression: $-2(x + 3) + 5(x - 2)$

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions has many real-world applications, including:

• Physics: Simplifying expressions is used to solve problems involving motion and energy.
• Engineering: Simplifying expressions is used to design and optimize systems.
• Economics: Simplifying expressions is used to model and analyze economic systems.

Conclusion

In conclusion, simplifying expressions is a crucial skill that helps us solve equations and inequalities. By following the steps outlined in this article, we can simplify any expression and make it easier to work with. Remember to always distribute the signs, combine like terms, combine constants, and simplify the expression by combining the results of the previous steps. With practice and patience, you can become proficient in simplifying expressions and apply it to real-world problems.