Select The Correct Answer.What Is The Justification For Step 3 In The Solution Process?$[ \begin Array}{rl} & \frac{3}{3} H - \frac{15}{2} = \frac{1}{5} H \ \text{Step 1 & \frac 23}{10} H - \frac{15}{2} = 0 \ \text{Step 2 & \frac{23}{10} H =

Introduction

In solving mathematical equations, it is essential to understand the reasoning behind each step. This not only helps in verifying the accuracy of the solution but also enhances the problem-solving skills. In this article, we will delve into the justification for step 3 in the solution process of a given equation.

The Equation

The given equation is:

$\frac{3}{3} h - \frac{15}{2} = \frac{1}{5} h$

Step 1: Isolating the Variable

The first step in solving the equation is to isolate the variable $h$. To do this, we need to get rid of the constant term on the left-hand side of the equation.

$\frac{23}{10} h - \frac{15}{2} = 0$

Step 2: Adding the Constant Term

In the next step, we add the constant term to both sides of the equation to isolate the term containing the variable.

$\frac{23}{10} h = \frac{15}{2}$

Step 3: Multiplying by the Reciprocal

The justification for step 3 in the solution process is to multiply both sides of the equation by the reciprocal of the coefficient of the variable. In this case, the coefficient of $h$ is $\frac{23}{10}$, and its reciprocal is $\frac{10}{23}$.

$\frac{10}{23} \cdot \frac{23}{10} h = \frac{10}{23} \cdot \frac{15}{2}$

Justification for Step 3

The justification for step 3 is based on the property of equality, which states that if two expressions are equal, then their product with the same non-zero factor is also equal. In this case, we multiply both sides of the equation by $\frac{10}{23}$, which is the reciprocal of the coefficient of $h$. This allows us to eliminate the coefficient and isolate the variable.

Simplifying the Equation

After multiplying both sides of the equation by $\frac{10}{23}$, we get:

$h = \frac{150}{23}$

Conclusion

In conclusion, the justification for step 3 in the solution process is to multiply both sides of the equation by the reciprocal of the coefficient of the variable. This allows us to eliminate the coefficient and isolate the variable, making it easier to solve the equation. By understanding the reasoning behind each step, we can enhance our problem-solving skills and verify the accuracy of the solution.

Additional Tips and Tricks

• When solving equations, it is essential to understand the reasoning behind each step.
• The property of equality states that if two expressions are equal, then their product with the same non-zero factor is also equal.
• Multiplying both sides of the equation by the reciprocal of the coefficient of the variable allows us to eliminate the coefficient and isolate the variable.

Common Mistakes to Avoid

• Failing to understand the reasoning behind each step can lead to incorrect solutions.
• Not using the property of equality can result in incorrect products.
• Not multiplying both sides of the equation by the reciprocal of the coefficient of the variable can lead to incorrect solutions.

Real-World Applications

Understanding the justification for step 3 in the solution process has real-world applications in various fields, such as:

• Physics: In solving equations related to motion, energy, and momentum.
• Engineering: In designing and optimizing systems, such as electrical circuits and mechanical systems.
• Economics: In modeling and analyzing economic systems, such as supply and demand.

Final Thoughts

Q: What is the purpose of step 3 in the solution process?

A: The purpose of step 3 in the solution process is to multiply both sides of the equation by the reciprocal of the coefficient of the variable. This allows us to eliminate the coefficient and isolate the variable, making it easier to solve the equation.

Q: Why do we need to multiply by the reciprocal of the coefficient?

A: We need to multiply by the reciprocal of the coefficient because it allows us to eliminate the coefficient and isolate the variable. This is based on the property of equality, which states that if two expressions are equal, then their product with the same non-zero factor is also equal.

Q: What is the property of equality?

A: The property of equality states that if two expressions are equal, then their product with the same non-zero factor is also equal. This means that if we multiply both sides of an equation by the same non-zero factor, the equation remains true.

Q: How do we know when to multiply by the reciprocal of the coefficient?

A: We know when to multiply by the reciprocal of the coefficient when we need to eliminate the coefficient and isolate the variable. This is typically the case when we are solving equations with variables on both sides.

Q: What are some common mistakes to avoid when multiplying by the reciprocal of the coefficient?

A: Some common mistakes to avoid when multiplying by the reciprocal of the coefficient include:

• Failing to multiply both sides of the equation by the reciprocal of the coefficient.
• Multiplying by the wrong reciprocal of the coefficient.
• Not checking the solution to ensure that it is correct.

Q: How does understanding the justification for step 3 in the solution process help in real-world applications?

A: Understanding the justification for step 3 in the solution process has real-world applications in various fields, such as:

• Physics: In solving equations related to motion, energy, and momentum.
• Engineering: In designing and optimizing systems, such as electrical circuits and mechanical systems.
• Economics: In modeling and analyzing economic systems, such as supply and demand.

Q: What are some additional tips and tricks for solving equations?

A: Some additional tips and tricks for solving equations include:

• Using the property of equality to eliminate coefficients and isolate variables.
• Checking the solution to ensure that it is correct.
• Using algebraic manipulations to simplify equations and make them easier to solve.

Q: How can I practice solving equations and improve my problem-solving skills?

A: You can practice solving equations and improve your problem-solving skills by:

• Working through practice problems and exercises.
• Using online resources and tools to help with problem-solving.
• Joining a study group or seeking help from a tutor or mentor.

Q: What are some common types of equations that require the use of step 3 in the solution process?

A: Some common types of equations that require the use of step 3 in the solution process include:

• Linear equations with variables on both sides.
• Quadratic equations with variables on both sides.
• Systems of equations with multiple variables.

Q: How can I apply the justification for step 3 in the solution process to other areas of mathematics?

A: You can apply the justification for step 3 in the solution process to other areas of mathematics by:

• Using the property of equality to eliminate coefficients and isolate variables in other types of equations.
• Applying algebraic manipulations to simplify equations and make them easier to solve.
• Using the justification for step 3 in the solution process to solve systems of equations and other types of mathematical problems.