Solve For { J $} . . . { \frac{3}{5} J = 6 \}
Introduction
Solving for j in the equation 3/5j = 6 is a fundamental problem in algebra that requires a step-by-step approach to isolate the variable j. In this article, we will guide you through the process of solving for j using basic algebraic operations.
Understanding the Equation
The given equation is 3/5j = 6. To solve for j, we need to isolate the variable j on one side of the equation. The equation can be rewritten as:
3/5j = 6
Step 1: Multiply Both Sides by 5
To eliminate the fraction, we can multiply both sides of the equation by 5. This will help us get rid of the denominator.
5 * (3/5j) = 5 * 6
Step 3: Simplify the Equation
Multiplying both sides of the equation by 5, we get:
3j = 30
Step 4: Divide Both Sides by 3
To isolate the variable j, we need to divide both sides of the equation by 3.
(3j) / 3 = 30 / 3
Step 5: Simplify the Equation
Dividing both sides of the equation by 3, we get:
j = 10
Conclusion
In this article, we have solved for j in the equation 3/5j = 6 using basic algebraic operations. We started by multiplying both sides of the equation by 5 to eliminate the fraction, then simplified the equation, and finally divided both sides by 3 to isolate the variable j. The final answer is j = 10.
Tips and Tricks
- When solving for a variable, always start by isolating the variable on one side of the equation.
- Use basic algebraic operations such as multiplication, division, addition, and subtraction to simplify the equation.
- Make sure to check your work by plugging the solution back into the original equation.
Real-World Applications
Solving for j in the equation 3/5j = 6 has real-world applications in various fields such as physics, engineering, and economics. For example, in physics, the equation can be used to calculate the velocity of an object, while in engineering, it can be used to calculate the stress on a material.
Common Mistakes
- Not isolating the variable on one side of the equation.
- Not using basic algebraic operations to simplify the equation.
- Not checking the work by plugging the solution back into the original equation.
Final Answer
The final answer is j = 10.
Introduction
In our previous article, we solved for j in the equation 3/5j = 6 using basic algebraic operations. In this article, we will answer some frequently asked questions related to solving for j in the equation 3/5j = 6.
Q: What is the first step in solving for j in the equation 3/5j = 6?
A: The first step in solving for j in the equation 3/5j = 6 is to multiply both sides of the equation by 5 to eliminate the fraction.
Q: Why do we need to multiply both sides of the equation by 5?
A: We need to multiply both sides of the equation by 5 to eliminate the fraction. This will help us get rid of the denominator and make it easier to isolate the variable j.
Q: What is the next step after multiplying both sides of the equation by 5?
A: After multiplying both sides of the equation by 5, we need to simplify the equation. This involves combining like terms and getting rid of any unnecessary operations.
Q: How do we simplify the equation 3j = 30?
A: We can simplify the equation 3j = 30 by dividing both sides of the equation by 3. This will help us isolate the variable j.
Q: What is the final answer to the equation 3/5j = 6?
A: The final answer to the equation 3/5j = 6 is j = 10.
Q: What are some common mistakes to avoid when solving for j in the equation 3/5j = 6?
A: Some common mistakes to avoid when solving for j in the equation 3/5j = 6 include not isolating the variable on one side of the equation, not using basic algebraic operations to simplify the equation, and not checking the work by plugging the solution back into the original equation.
Q: How can I apply the concept of solving for j in the equation 3/5j = 6 to real-world problems?
A: The concept of solving for j in the equation 3/5j = 6 can be applied to real-world problems in various fields such as physics, engineering, and economics. For example, in physics, the equation can be used to calculate the velocity of an object, while in engineering, it can be used to calculate the stress on a material.
Q: What are some tips and tricks for solving for j in the equation 3/5j = 6?
A: Some tips and tricks for solving for j in the equation 3/5j = 6 include starting by isolating the variable on one side of the equation, using basic algebraic operations to simplify the equation, and checking the work by plugging the solution back into the original equation.
Conclusion
In this article, we have answered some frequently asked questions related to solving for j in the equation 3/5j = 6. We have covered topics such as the first step in solving for j, why we need to multiply both sides of the equation by 5, and how to simplify the equation. We have also provided some tips and tricks for solving for j in the equation 3/5j = 6 and discussed how to apply the concept to real-world problems.
Final Answer
The final answer is j = 10.
Additional Resources
- For more information on solving for j in the equation 3/5j = 6, please refer to our previous article.
- For more information on algebraic operations, please refer to our article on basic algebraic operations.
- For more information on real-world applications of solving for j in the equation 3/5j = 6, please refer to our article on real-world applications of algebra.