Find The Value Of $Z$ In The Following Equation: $8Z = 64$A. 56 B. 8 C. 72 D. 512
Introduction
In mathematics, solving for a variable is a fundamental concept that is essential for understanding various mathematical operations and equations. In this article, we will focus on solving for the variable Z in the equation 8Z = 64. This equation is a simple linear equation that can be solved using basic algebraic operations.
Understanding the Equation
The equation 8Z = 64 is a linear equation that involves a single variable, Z. The equation states that 8 times Z is equal to 64. To solve for Z, we need to isolate the variable Z on one side of the equation.
Solving for Z
To solve for Z, we can use the following steps:
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Divide both sides of the equation by 8: This will isolate the variable Z on one side of the equation.
Simplifying the equation, we get:
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Check the solution: To verify that our solution is correct, we can substitute the value of Z back into the original equation and check if it is true.
Simplifying the equation, we get:
Since the equation is true, our solution is correct.
Conclusion
In this article, we solved for the variable Z in the equation 8Z = 64. We used basic algebraic operations to isolate the variable Z on one side of the equation and found that Z = 8. This solution can be verified by substituting the value of Z back into the original equation.
Answer
The correct answer is B. 8.
Why is this important?
Solving for a variable is an essential skill in mathematics that is used in various fields, including science, engineering, and economics. By understanding how to solve for a variable, individuals can analyze and solve complex mathematical problems, which is critical for making informed decisions and solving real-world problems.
Real-World Applications
Solving for a variable has numerous real-world applications, including:
- Science: Solving for a variable is used to analyze and understand scientific data, which is critical for making informed decisions and solving complex scientific problems.
- Engineering: Solving for a variable is used to design and optimize complex systems, such as bridges, buildings, and electronic circuits.
- Economics: Solving for a variable is used to analyze and understand economic data, which is critical for making informed decisions and solving complex economic problems.
Tips and Tricks
Here are some tips and tricks for solving for a variable:
- Use basic algebraic operations: Solving for a variable involves using basic algebraic operations, such as addition, subtraction, multiplication, and division.
- Isolate the variable: To solve for a variable, you need to isolate the variable on one side of the equation.
- Check the solution: To verify that your solution is correct, you need to substitute the value of the variable back into the original equation and check if it is true.
Common Mistakes
Here are some common mistakes to avoid when solving for a variable:
- Not isolating the variable: Failing to isolate the variable on one side of the equation can lead to incorrect solutions.
- Not checking the solution: Failing to verify that the solution is correct can lead to incorrect conclusions.
- Using complex algebraic operations: Using complex algebraic operations can lead to incorrect solutions and make it difficult to verify the solution.
Conclusion
Solving for a variable is an essential skill in mathematics that is used in various fields, including science, engineering, and economics. By understanding how to solve for a variable, individuals can analyze and solve complex mathematical problems, which is critical for making informed decisions and solving real-world problems.
Introduction
In our previous article, we solved for the variable Z in the equation 8Z = 64. In this article, we will provide a Q&A guide to help you understand the concept of solving for a variable and how to apply it to real-world problems.
Q&A
Q: What is the value of Z in the equation 8Z = 64?
A: The value of Z in the equation 8Z = 64 is 8.
Q: How do I solve for a variable in a linear equation?
A: To solve for a variable in a linear equation, you need to isolate the variable on one side of the equation. This can be done by using basic algebraic operations, such as addition, subtraction, multiplication, and division.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation that involves a single variable and has a degree of 1. A quadratic equation is an equation that involves a single variable and has a degree of 2.
Q: How do I check if my solution is correct?
A: To check if your solution is correct, you need to substitute the value of the variable back into the original equation and check if it is true.
Q: What are some common mistakes to avoid when solving for a variable?
A: Some common mistakes to avoid when solving for a variable include:
- Not isolating the variable on one side of the equation
- Not checking the solution
- Using complex algebraic operations
Q: How do I apply the concept of solving for a variable to real-world problems?
A: The concept of solving for a variable can be applied to real-world problems in various fields, including science, engineering, and economics. For example, in science, solving for a variable can help you analyze and understand scientific data. In engineering, solving for a variable can help you design and optimize complex systems.
Q: What are some real-world applications of solving for a variable?
A: Some real-world applications of solving for a variable include:
- Analyzing and understanding scientific data
- Designing and optimizing complex systems
- Analyzing and understanding economic data
Q: How do I use technology to solve for a variable?
A: There are various technologies that can be used to solve for a variable, including calculators, computer software, and online tools.
Q: What are some tips and tricks for solving for a variable?
A: Some tips and tricks for solving for a variable include:
- Using basic algebraic operations
- Isolating the variable on one side of the equation
- Checking the solution
Conclusion
Solving for a variable is an essential skill in mathematics that is used in various fields, including science, engineering, and economics. By understanding how to solve for a variable, individuals can analyze and solve complex mathematical problems, which is critical for making informed decisions and solving real-world problems.
Additional Resources
For additional resources on solving for a variable, including videos, tutorials, and practice problems, please visit the following websites:
- Khan Academy: www.khanacademy.org
- Mathway: www.mathway.com
- Wolfram Alpha: www.wolframalpha.com
Final Thoughts
Solving for a variable is a fundamental concept in mathematics that is used in various fields. By understanding how to solve for a variable, individuals can analyze and solve complex mathematical problems, which is critical for making informed decisions and solving real-world problems.