Solve For { H $}$.(vii) { \frac{2h}{3} = 4$}$
Introduction
In this article, we will focus on solving for the variable h in the given equation 2h/3 = 4. This equation is a simple algebraic equation that can be solved using basic algebraic operations. We will break down the solution step by step and provide a clear explanation of each step.
Understanding the Equation
The given equation is 2h/3 = 4. This equation is a linear equation, where the variable h is multiplied by 2 and then divided by 3, resulting in an equal value of 4.
Step 1: Multiply Both Sides by 3
To solve for h, we need to isolate the variable h on one side of the equation. We can do this by multiplying both sides of the equation by 3, which will eliminate the fraction.
\frac{2h}{3} = 4
\implies 2h = 4 \times 3
\implies 2h = 12
Step 2: Divide Both Sides by 2
Now that we have eliminated the fraction, we can divide both sides of the equation by 2 to isolate the variable h.
2h = 12
\implies h = \frac{12}{2}
\implies h = 6
Conclusion
In this article, we have solved for the variable h in the equation 2h/3 = 4. We have broken down the solution into two steps: multiplying both sides of the equation by 3 and then dividing both sides by 2. By following these steps, we have isolated the variable h and found its value to be 6.
Tips and Variations
- To solve for h in the equation 2h/3 = 4, we can also use the inverse operation of multiplication, which is division.
- We can also use the distributive property to simplify the equation before solving for h.
- If the equation is more complex, we may need to use more advanced algebraic operations, such as factoring or using the quadratic formula.
Real-World Applications
Solving for h in the equation 2h/3 = 4 has many real-world applications. For example:
- In physics, we may need to solve for the distance traveled by an object, which can be represented by the variable h.
- In engineering, we may need to solve for the stress or strain on a material, which can be represented by the variable h.
- In finance, we may need to solve for the interest rate or the present value of a future cash flow, which can be represented by the variable h.
Common Mistakes
When solving for h in the equation 2h/3 = 4, some common mistakes to avoid include:
- Not multiplying both sides of the equation by 3, which can result in an incorrect solution.
- Not dividing both sides of the equation by 2, which can result in an incorrect solution.
- Not checking the solution for consistency with the original equation, which can result in an incorrect solution.
Conclusion
Introduction
In our previous article, we solved for the variable h in the equation 2h/3 = 4. In this article, we will provide a Q&A section to help clarify any doubts or questions that readers may have.
Q: What is the value of h in the equation 2h/3 = 4?
A: The value of h in the equation 2h/3 = 4 is 6.
Q: How do I solve for h in the equation 2h/3 = 4?
A: To solve for h in the equation 2h/3 = 4, you can follow these steps:
- Multiply both sides of the equation by 3 to eliminate the fraction.
- Divide both sides of the equation by 2 to isolate the variable h.
Q: What if the equation is more complex, such as 2h/3 + 2 = 4?
A: If the equation is more complex, such as 2h/3 + 2 = 4, you can use the same steps as before to solve for h. However, you may need to use more advanced algebraic operations, such as subtracting 2 from both sides of the equation before solving for h.
Q: Can I use a calculator to solve for h in the equation 2h/3 = 4?
A: Yes, you can use a calculator to solve for h in the equation 2h/3 = 4. However, it's always a good idea to check your solution by plugging it back into the original equation to ensure that it's correct.
Q: What if I get a different answer when solving for h in the equation 2h/3 = 4?
A: If you get a different answer when solving for h in the equation 2h/3 = 4, it's possible that you made a mistake in your calculations. Double-check your work and make sure that you followed the correct steps.
Q: Can I apply the solution to the equation 2h/3 = 4 to real-world problems?
A: Yes, you can apply the solution to the equation 2h/3 = 4 to real-world problems. For example, if you're working with a physics problem and you need to find the distance traveled by an object, you can use the solution to the equation 2h/3 = 4 to find the value of h.
Q: What are some common mistakes to avoid when solving for h in the equation 2h/3 = 4?
A: Some common mistakes to avoid when solving for h in the equation 2h/3 = 4 include:
- Not multiplying both sides of the equation by 3, which can result in an incorrect solution.
- Not dividing both sides of the equation by 2, which can result in an incorrect solution.
- Not checking the solution for consistency with the original equation, which can result in an incorrect solution.
Conclusion
In conclusion, solving for h in the equation 2h/3 = 4 is a simple algebraic operation that can be solved using basic algebraic operations. By following the steps outlined in this article and avoiding common mistakes, you can find the value of h and apply it to real-world problems.
Additional Resources
If you're looking for additional resources to help you solve for h in the equation 2h/3 = 4, you may want to check out the following:
- Online algebra tutorials and videos
- Algebra textbooks and workbooks
- Online calculators and math tools
Final Thoughts
Solving for h in the equation 2h/3 = 4 is just one example of how algebra can be used to solve real-world problems. By practicing and applying algebraic operations, you can become more confident and proficient in solving equations and applying them to real-world situations.