A Simple Algebraic Equation

Oct 13, 2025 by talynt.org 62 views

A Simple Algebraic Equation

In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for the variable $$w$$ in a simple algebraic equation.

The Equation

The given equation is:

${ 9 = 3 \times w }$

This equation states that the product of 3 and $$w$$ is equal to 9. To solve for $$w$$, we need to isolate $$w$$ on one side of the equation.

Solving for $$w$$

To solve for $$w$$, we can use the inverse operation of multiplication, which is division. We can divide both sides of the equation by 3 to isolate $$w$$.

${ \frac{9}{3} = \frac{3 \times w}{3} }$

Using the property of division, we can simplify the equation as follows:

${ 3 = w }$

Therefore, the value of $$w$$ is 3.

Understanding the Solution

In this solution, we used the inverse operation of multiplication to isolate $$w$$ on one side of the equation. This is a fundamental concept in algebra, and it is essential to understand how to use inverse operations to solve equations.

Real-World Applications

Solving for a variable is a crucial skill in many real-world applications, including science, engineering, and economics. For example, in physics, you may need to solve for the velocity of an object given its acceleration and time. In finance, you may need to solve for the interest rate given the principal amount, time, and interest earned.

Conclusion

Solving for $$w$$: A Step-by-Step Guide

Step 1: Write Down the Equation

The given equation is:

${ 9 = 3 \times w }$

Step 2: Identify the Inverse Operation

The inverse operation of multiplication is division. We can divide both sides of the equation by 3 to isolate $$w$$.

Step 3: Simplify the Equation

Using the property of division, we can simplify the equation as follows:

${ 3 = w }$

Step 4: Check the Solution

To check the solution, we can plug in the value of $$w$$ back into the original equation:

${ 9 = 3 \times 3 }$

${ 9 = 9 }$

This confirms that the solution is correct.

Common Mistakes to Avoid

1. Not Using the Inverse Operation

One common mistake is not using the inverse operation to isolate the variable. In this case, we need to use division to isolate $$w$$.

2. Not Simplifying the Equation

Another common mistake is not simplifying the equation after using the inverse operation. In this case, we need to simplify the equation to get the final solution.

3. Not Checking the Solution

Finally, it's essential to check the solution by plugging in the value of $$w$$ back into the original equation.

Conclusion

Solving for $$w$$ in the given equation is a simple algebraic equation that involves isolating the variable on one side of the equation. By using the inverse operation of multiplication, we can easily solve for $$w$$ and understand the concept of solving for a variable. Remember to avoid common mistakes such as not using the inverse operation, not simplifying the equation, and not checking the solution.

Frequently Asked Questions

Q: What is the value of $$w$$?

A: The value of $$w$$ is 3.

Q: How do I solve for $$w$$?

A: To solve for $$w$$, you can use the inverse operation of multiplication, which is division. Divide both sides of the equation by 3 to isolate $$w$$.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division.

Q: Why is it essential to check the solution?

A: It's essential to check the solution by plugging in the value of $$w$$ back into the original equation to confirm that the solution is correct.

Conclusion

Frequently Asked Questions

Q: What is the value of $$w$$?

A: The value of $$w$$ is 3.

Q: How do I solve for $$w$$?

A: To solve for $$w$$, you can use the inverse operation of multiplication, which is division. Divide both sides of the equation by 3 to isolate $$w$$.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division.

Q: Why is it essential to check the solution?

A: It's essential to check the solution by plugging in the value of $$w$$ back into the original equation to confirm that the solution is correct.

Advanced Questions and Answers

Q: How do I solve for $$w$$ in an equation with fractions?

A: To solve for $$w$$ in an equation with fractions, multiply both sides of the equation by the least common multiple of the denominators to eliminate the fractions.

Q: How do I solve for $$w$$ in an equation with decimals?

A: To solve for $$w$$ in an equation with decimals, multiply both sides of the equation by 10 to eliminate the decimals.

Q: How do I solve for $$w$$ in an equation with exponents?

A: To solve for $$w$$ in an equation with exponents, use the power rule of exponents to simplify the equation and then isolate $$w$$.

Conclusion

Additional Resources

Final Thoughts

Solving for $$w$$ in the given equation is a fundamental concept in algebra that involves isolating the variable on one side of the equation. By using the inverse operation of multiplication, we can easily solve for $$w$$ and understand the concept of solving for a variable. Remember to practice regularly and seek help when needed to become proficient in solving algebraic equations.