The Importance of Isolating the Term

Oct 13, 2025 by magicalceylontours.com 67 views

Understanding the Problem

When dealing with algebraic equations, isolating a specific term is a crucial step in solving for the unknown variable. In this case, we are given the equation $\frac{f}{3} + 22 = 17$ , and we need to isolate the term $\frac{f}{3}$ . To do this, we must perform a series of operations on both sides of the equation to eliminate the constant term and isolate the variable term.

The Importance of Isolating the Term

Isolating the term $\frac{f}{3}$ is essential in solving for the value of $f$ . By isolating the term, we can determine the value of $f$ by performing a simple operation. In this case, we can multiply both sides of the equation by 3 to eliminate the fraction and solve for $f$ .

Steps to Isolate the Term

To isolate the term $\frac{f}{3}$ , we need to perform the following steps:

Step 1: Subtract 22 from Both Sides

The first step in isolating the term $\frac{f}{3}$ is to subtract 22 from both sides of the equation. This will eliminate the constant term on the left-hand side of the equation.

$\frac{f}{3} + 22 - 22 = 17 - 22$

$\frac{f}{3} = -5$

Step 2: Multiply Both Sides by 3

Once we have isolated the term $\frac{f}{3}$ , we can multiply both sides of the equation by 3 to eliminate the fraction and solve for $f$ .

$\frac{f}{3} \times 3 = -5 \times 3$

$f = -15$

Conclusion

In conclusion, to isolate the term $\frac{f}{3}$ in the equation $\frac{f}{3} + 22 = 17$ , we need to perform a series of operations on both sides of the equation. By subtracting 22 from both sides and then multiplying both sides by 3, we can eliminate the constant term and isolate the variable term. This allows us to solve for the value of $f$ by performing a simple operation.

Tips and Tricks

When dealing with algebraic equations, it's essential to isolate the variable term to solve for the unknown variable.
To isolate a term, you need to perform a series of operations on both sides of the equation to eliminate the constant term.
When multiplying or dividing both sides of an equation by a constant, make sure to multiply or divide both sides by the same constant.

Common Mistakes to Avoid

When isolating a term, make sure to perform the correct operations on both sides of the equation.
Avoid multiplying or dividing both sides of an equation by a variable or an expression that contains the variable.
Make sure to check your work by plugging the solution back into the original equation to ensure that it's true.

Real-World Applications

Isolating a term is a crucial step in solving algebraic equations, and it has numerous real-world applications. For example, in physics, isolating a term can help us determine the value of a variable that represents a physical quantity, such as velocity or acceleration. In engineering, isolating a term can help us design and optimize systems, such as electrical circuits or mechanical systems.

Final Thoughts

In conclusion, isolating the term $\frac{f}{3}$ in the equation $\frac{f}{3} + 22 = 17$ requires a series of operations on both sides of the equation. By subtracting 22 from both sides and then multiplying both sides by 3, we can eliminate the constant term and isolate the variable term. This allows us to solve for the value of $f$ by performing a simple operation.

Frequently Asked Questions

Q: What is the first step in isolating the term $\frac{f}{3}$ in the equation $\frac{f}{3} + 22 = 17$ ?

A: The first step in isolating the term $\frac{f}{3}$ is to subtract 22 from both sides of the equation. This will eliminate the constant term on the left-hand side of the equation.

Q: Why do we need to subtract 22 from both sides of the equation?

A: We need to subtract 22 from both sides of the equation to eliminate the constant term on the left-hand side of the equation. This will allow us to isolate the term $\frac{f}{3}$ .

Q: What is the next step in isolating the term $\frac{f}{3}$ ?

A: The next step in isolating the term $\frac{f}{3}$ is to multiply both sides of the equation by 3. This will eliminate the fraction and allow us to solve for $f$ .

Q: Why do we need to multiply both sides of the equation by 3?

A: We need to multiply both sides of the equation by 3 to eliminate the fraction and allow us to solve for $f$ . This will give us the value of $f$ .

Q: What is the final step in isolating the term $\frac{f}{3}$ ?

A: The final step in isolating the term $\frac{f}{3}$ is to simplify the equation and solve for $f$ . This will give us the value of $f$ .

Q: What are some common mistakes to avoid when isolating a term?

A: Some common mistakes to avoid when isolating a term include:

Multiplying or dividing both sides of an equation by a variable or an expression that contains the variable.
Not checking the work by plugging the solution back into the original equation to ensure that it's true.
Not following the order of operations when simplifying the equation.

Q: What are some real-world applications of isolating a term?

A: Some real-world applications of isolating a term include:

Solving algebraic equations in physics and engineering.
Designing and optimizing systems, such as electrical circuits or mechanical systems.
Determining the value of a variable that represents a physical quantity, such as velocity or acceleration.

Q: How can I practice isolating a term?

A: You can practice isolating a term by working through examples and exercises in your textbook or online resources. You can also try solving real-world problems that involve isolating a term.

Q: What are some tips for isolating a term?

A: Some tips for isolating a term include:

Following the order of operations when simplifying the equation.
Checking the work by plugging the solution back into the original equation to ensure that it's true.
Using a calculator or computer program to check the solution and ensure that it's accurate.