Solve The Equation \[$-5(-9x - 10) + 6 = -3(x + 4) - 316\$\] Algebraically.Answer As A Reduced Fraction Only.\[$x = \, \square\$\]

$$

Introduction

Solving equations algebraically is a fundamental concept in mathematics, and it requires a deep understanding of algebraic expressions and operations. In this article, we will focus on solving a specific equation, ${-5(-9x - 10) + 6 = -3(x + 4) - 316,}$ algebraically. We will break down the solution step by step, using various algebraic techniques to simplify the equation and isolate the variable x.

Step 1: Distribute the Negative Sign

The first step in solving the equation is to distribute the negative sign to the terms inside the parentheses. This will simplify the equation and make it easier to work with.

${-5(-9x - 10) + 6 = -3(x + 4) - 316}$

Distributing the negative sign, we get:

${45x + 50 + 6 = -3x - 12 - 316}$

Step 2: Combine Like Terms

The next step is to combine like terms on both sides of the equation. This will further simplify the equation and make it easier to solve.

${45x + 56 = -3x - 328}$

Step 3: Add 3x to Both Sides

To isolate the variable x, we need to get all the x terms on one side of the equation. We can do this by adding 3x to both sides of the equation.

${45x + 56 + 3x = -3x - 328 + 3x}$

This simplifies to:

${48x + 56 = -328}$

Step 4: Subtract 56 from Both Sides

Next, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 56 from both sides of the equation.

${48x + 56 - 56 = -328 - 56}$

This simplifies to:

${48x = -384}$

Step 5: Divide Both Sides by 48

Finally, we need to isolate the variable x by dividing both sides of the equation by 48.

${48x / 48 = -384 / 48}$

This simplifies to:

${x = -8}$

Conclusion

In this article, we solved the equation ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$ algebraically. We broke down the solution step by step, using various algebraic techniques to simplify the equation and isolate the variable x. The final solution is x = -8.

Final Answer

The final answer is x = -8.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Distribute the negative sign: ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$
2. Combine like terms: ${45x + 56 = -3x - 328}$
3. Add 3x to both sides: ${48x + 56 = -328}$
4. Subtract 56 from both sides: ${48x = -384}$
5. Divide both sides by 48: ${x = -8}$

Algebraic Techniques Used

In this article, we used the following algebraic techniques to solve the equation:

• Distributing the negative sign
• Combining like terms
• Adding and subtracting terms
• Dividing both sides of the equation by a constant

Importance of Algebraic Techniques

Algebraic techniques are essential in solving equations algebraically. They help to simplify the equation, isolate the variable, and find the solution. In this article, we used various algebraic techniques to solve the equation and find the final solution.

Real-World Applications

Solving equations algebraically has many real-world applications. It is used in various fields such as physics, engineering, economics, and computer science. In these fields, equations are used to model real-world problems, and solving them algebraically is essential to find the solution.

Conclusion

In conclusion, solving the equation ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$ algebraically requires a deep understanding of algebraic expressions and operations. We used various algebraic techniques to simplify the equation and isolate the variable x. The final solution is x = -8.

$$

Introduction

In our previous article, we solved the equation ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$ algebraically. In this article, we will answer some frequently asked questions (FAQs) about solving this equation.

Q: What is the first step in solving the equation?

A: The first step in solving the equation is to distribute the negative sign to the terms inside the parentheses.

Q: Why do we need to combine like terms?

A: We need to combine like terms to simplify the equation and make it easier to work with. Combining like terms helps to eliminate unnecessary variables and makes the equation more manageable.

Q: What is the purpose of adding 3x to both sides of the equation?

A: The purpose of adding 3x to both sides of the equation is to isolate the variable x. By adding 3x to both sides, we are able to get all the x terms on one side of the equation.

Q: Why do we need to subtract 56 from both sides of the equation?

A: We need to subtract 56 from both sides of the equation to get rid of the constant term on the left side of the equation. This helps to simplify the equation and make it easier to solve.

Q: What is the final step in solving the equation?

A: The final step in solving the equation is to divide both sides of the equation by 48. This helps to isolate the variable x and find the final solution.

Q: What are some common mistakes to avoid when solving the equation?

A: Some common mistakes to avoid when solving the equation include:

• Not distributing the negative sign correctly
• Not combining like terms
• Not adding or subtracting terms correctly
• Not dividing both sides of the equation by the correct constant

Q: How can I practice solving equations like this one?

A: You can practice solving equations like this one by working through example problems and exercises. You can also try solving different types of equations, such as linear and quadratic equations.

Q: What are some real-world applications of solving equations like this one?

A: Solving equations like this one has many real-world applications, including:

• Modeling population growth and decline
• Analyzing financial data
• Solving optimization problems
• Modeling physical systems

Q: Can I use a calculator to solve the equation?

A: Yes, you can use a calculator to solve the equation. However, it's also important to understand the algebraic techniques used to solve the equation, as this will help you to solve more complex equations in the future.

Q: How can I check my answer to make sure it's correct?

A: You can check your answer by plugging it back into the original equation and making sure that it's true. You can also use a calculator to check your answer.

Conclusion

In conclusion, solving the equation ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$ algebraically requires a deep understanding of algebraic expressions and operations. By following the steps outlined in this article, you can solve the equation and find the final solution. Remember to practice solving equations like this one to build your skills and confidence.

Final Answer

The final answer is x = -8.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Distribute the negative sign: ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$
2. Combine like terms: ${45x + 56 = -3x - 328}$
3. Add 3x to both sides: ${48x + 56 = -328}$
4. Subtract 56 from both sides: ${48x = -384}$
5. Divide both sides by 48: ${x = -8}$

Algebraic Techniques Used

In this article, we used the following algebraic techniques to solve the equation:

• Distributing the negative sign
• Combining like terms
• Adding and subtracting terms
• Dividing both sides of the equation by a constant

Importance of Algebraic Techniques

Algebraic techniques are essential in solving equations algebraically. They help to simplify the equation, isolate the variable, and find the solution. In this article, we used various algebraic techniques to solve the equation and find the final solution.

Real-World Applications

Solving equations algebraically has many real-world applications. It is used in various fields such as physics, engineering, economics, and computer science. In these fields, equations are used to model real-world problems, and solving them algebraically is essential to find the solution.

Conclusion

In conclusion, solving the equation ${-5(-9x - 10) + 6 = -3(x + 4) - 316}$ algebraically requires a deep understanding of algebraic expressions and operations. By following the steps outlined in this article, you can solve the equation and find the final solution. Remember to practice solving equations like this one to build your skills and confidence.