What Is The Solution To This Equation?$7x - 8x - 9 = 76 - 40$A. $x = 3$ B. $x = 5$ C. $x = 4$ D. $x = 6$

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Understanding the Equation

The given equation is 7x−8x−9=76−407x - 8x - 9 = 76 - 40. To solve this equation, we need to follow the order of operations (PEMDAS) and simplify the equation step by step.

Simplifying the Equation

First, let's simplify the left-hand side of the equation by combining like terms:

7x−8x−9=−x−97x - 8x - 9 = -x - 9

Now, let's simplify the right-hand side of the equation by subtracting 40 from 76:

76−40=3676 - 40 = 36

So, the simplified equation is:

−x−9=36-x - 9 = 36

Isolating the Variable

To isolate the variable xx, we need to get rid of the negative sign in front of the xx. We can do this by adding 9 to both sides of the equation:

−x−9+9=36+9-x - 9 + 9 = 36 + 9

This simplifies to:

−x=45-x = 45

Solving for x

To solve for xx, we need to get rid of the negative sign in front of the xx. We can do this by multiplying both sides of the equation by -1:

−x×−1=45×−1-x \times -1 = 45 \times -1

This simplifies to:

x=−45x = -45

Checking the Answer Choices

Now that we have solved for xx, let's check the answer choices to see which one matches our solution:

A. x=3x = 3 B. x=5x = 5 C. x=4x = 4 D. x=6x = 6

None of the answer choices match our solution, which is x=−45x = -45. However, we can see that the correct answer is not among the options provided.

Conclusion

In conclusion, the solution to the equation 7x−8x−9=76−407x - 8x - 9 = 76 - 40 is x=−45x = -45. Unfortunately, this answer is not among the options provided, which means that the question is flawed or the answer choices are incorrect.

Tips for Solving Equations

When solving equations, it's essential to follow the order of operations (PEMDAS) and simplify the equation step by step. Additionally, make sure to isolate the variable and check the answer choices to see which one matches your solution.

Common Mistakes to Avoid

When solving equations, some common mistakes to avoid include:

  • Not following the order of operations (PEMDAS)
  • Not simplifying the equation step by step
  • Not isolating the variable
  • Not checking the answer choices

By avoiding these common mistakes, you can ensure that you are solving equations correctly and accurately.

Real-World Applications

Solving equations is a fundamental skill that has numerous real-world applications. For example, in physics, equations are used to describe the motion of objects and predict their behavior. In finance, equations are used to calculate interest rates and investment returns. In engineering, equations are used to design and optimize systems.

Conclusion

In conclusion, solving equations is a critical skill that has numerous real-world applications. By following the order of operations (PEMDAS) and simplifying the equation step by step, you can ensure that you are solving equations correctly and accurately. Remember to isolate the variable and check the answer choices to see which one matches your solution.

Q: What is the order of operations (PEMDAS) and why is it important?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It's essential to follow the order of operations to ensure that we are solving equations correctly and accurately.

Q: How do I simplify an equation step by step?

A: To simplify an equation step by step, follow these steps:

  1. Combine like terms
  2. Simplify expressions inside parentheses
  3. Evaluate exponents
  4. Perform multiplication and division operations from left to right
  5. Perform addition and subtraction operations from left to right

Q: How do I isolate the variable in an equation?

A: To isolate the variable in an equation, follow these steps:

  1. Add or subtract the same value to both sides of the equation to get rid of any constants
  2. Multiply or divide both sides of the equation by the same value to get rid of any coefficients
  3. Use inverse operations to get rid of any remaining constants or coefficients

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2x + 3 = 5 is a linear equation. A quadratic equation is an equation in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, follow these steps:

  1. Factor the quadratic expression, if possible
  2. Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
  3. Use the method of substitution or elimination to solve the equation

Q: What is the quadratic formula and how do I use it?

A: The quadratic formula is a formula that allows us to solve quadratic equations. The formula is: x = (-b ± √(b^2 - 4ac)) / 2a. To use the quadratic formula, plug in the values of a, b, and c from the quadratic equation and simplify the expression.

Q: How do I check my answer to an equation?

A: To check your answer to an equation, plug the value of the variable back into the original equation and simplify the expression. If the expression is true, then your answer is correct.

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

A: Some common mistakes to avoid when solving equations include:

  • Not following the order of operations (PEMDAS)
  • Not simplifying the equation step by step
  • Not isolating the variable
  • Not checking the answer choices
  • Not using inverse operations to get rid of constants or coefficients

Q: How do I apply equations to real-world problems?

A: To apply equations to real-world problems, follow these steps:

  1. Identify the variables and constants in the problem
  2. Write an equation that represents the problem
  3. Solve the equation using the methods we have learned
  4. Check the answer to ensure that it makes sense in the context of the problem

Q: What are some examples of real-world applications of equations?

A: Some examples of real-world applications of equations include:

  • Physics: equations are used to describe the motion of objects and predict their behavior
  • Finance: equations are used to calculate interest rates and investment returns
  • Engineering: equations are used to design and optimize systems
  • Science: equations are used to model and predict the behavior of complex systems

Q: How do I practice solving equations?

A: To practice solving equations, try the following:

  • Work on practice problems from a textbook or online resource
  • Use online tools or apps to generate random equations and solve them
  • Join a study group or find a study partner to work on equations together
  • Take online quizzes or tests to assess your knowledge and skills

Q: What are some resources for learning more about equations?

A: Some resources for learning more about equations include:

  • Textbooks and online resources such as Khan Academy, Mathway, and Wolfram Alpha
  • Online courses and tutorials such as Coursera, edX, and Udemy
  • Study groups and online communities such as Reddit's r/learnmath and r/math
  • Professional development courses and workshops for teachers and educators