There Is A Step Missing From The Solution Below. Which Equation Is The Missing Step?$\[ \begin{array}{l} P = 10 - \sqrt{0.011 X + 13} \\ 5 = 10 - \sqrt{0.011 X + 13} \\ -5 = -\sqrt{0.011 X + 13} \\ ? \\ 12 = 0.011 X \\ 1091 \approx

The Missing Step in a Mathematical Equation: Identifying the Correct Sequence

Understanding the Problem

When solving mathematical equations, it's essential to follow a logical sequence of steps to arrive at the correct solution. However, sometimes, a crucial step may be overlooked, leading to confusion and incorrect conclusions. In this article, we'll examine a given mathematical equation and identify the missing step.

The Given Equation

The equation provided is:

$$P = 10 - \sqrt{0.011 x + 13}$$

We're asked to find the missing step in the solution process. To do this, let's start by analyzing the given equation and the steps that follow.

Step 1: Isolating the Square Root

The first step in solving the equation is to isolate the square root term. We can do this by subtracting 10 from both sides of the equation:

$$P - 10 = -\sqrt{0.011 x + 13}$$

This step is essential in preparing the equation for further manipulation.

Step 2: Squaring Both Sides

The next step is to square both sides of the equation to eliminate the square root:

$$(P - 10)^2 = (-\sqrt{0.011 x + 13})^2$$

This step is crucial in simplifying the equation and making it easier to solve.

Step 3: Simplifying the Equation

Now, let's simplify the equation by expanding the squared terms:

$$(P - 10)^2 = 0.011 x + 13$$

This step involves expanding the squared binomial and simplifying the resulting expression.

Step 4: Isolating the Variable

The next step is to isolate the variable x by subtracting 13 from both sides of the equation:

$$(P - 10)^2 - 13 = 0.011 x$$

This step is essential in preparing the equation for further manipulation.

Step 5: Dividing by the Coefficient

Finally, let's divide both sides of the equation by the coefficient of x (0.011) to solve for x:

$$\frac{(P - 10)^2 - 13}{0.011} = x$$

This step involves dividing both sides of the equation by the coefficient of x to isolate the variable.

The Missing Step

Now that we've analyzed the given equation and the steps that follow, let's identify the missing step. The correct sequence of steps is:

1. Isolate the square root term
2. Square both sides of the equation
3. Simplify the equation
4. Isolate the variable
5. Divide by the coefficient

However, the given equation only shows the first four steps. The missing step is the division by the coefficient (0.011) to solve for x.

The Correct Equation

The correct equation is:

$$\frac{(P - 10)^2 - 13}{0.011} = x$$

This equation represents the missing step in the solution process.

Conclusion

In conclusion, the missing step in the given mathematical equation is the division by the coefficient (0.011) to solve for x. By following the correct sequence of steps, we can arrive at the correct solution to the equation. This article has demonstrated the importance of following a logical sequence of steps when solving mathematical equations.

Discussion

The discussion category for this article is mathematics. The topic of the article is the missing step in a mathematical equation. The article provides a step-by-step analysis of the given equation and identifies the missing step.

Related Topics

• Mathematical equations
• Algebraic manipulation
• Problem-solving strategies
• Mathematical reasoning

Keywords

• Mathematical equations
• Algebraic manipulation
• Problem-solving strategies
• Mathematical reasoning
• Missing step
• Correct sequence of steps
• Division by coefficient
• Solving for x
  Frequently Asked Questions: The Missing Step in a Mathematical Equation

Introduction

In our previous article, we identified the missing step in a mathematical equation and provided a step-by-step analysis of the given equation. In this article, we'll answer some frequently asked questions related to the topic.

Q: What is the missing step in the given equation?

A: The missing step is the division by the coefficient (0.011) to solve for x.

Q: Why is the division by the coefficient important?

A: The division by the coefficient is essential in isolating the variable x and solving for its value.

Q: What is the correct sequence of steps to solve the equation?

A: The correct sequence of steps is:

1. Isolate the square root term
2. Square both sides of the equation
3. Simplify the equation
4. Isolate the variable
5. Divide by the coefficient

Q: Why is it essential to follow the correct sequence of steps?

A: Following the correct sequence of steps ensures that the equation is solved correctly and that the solution is accurate.

Q: What are some common mistakes that can occur when solving mathematical equations?

A: Some common mistakes that can occur when solving mathematical equations include:

• Not following the correct sequence of steps
• Not isolating the variable correctly
• Not simplifying the equation correctly
• Not checking the solution for accuracy

Q: How can I avoid making mistakes when solving mathematical equations?

A: To avoid making mistakes when solving mathematical equations, it's essential to:

• Follow the correct sequence of steps
• Check the solution for accuracy
• Simplify the equation correctly
• Isolate the variable correctly

Q: What are some tips for solving mathematical equations?

A: Some tips for solving mathematical equations include:

• Read the equation carefully and understand what is being asked
• Break down the equation into smaller parts and solve each part separately
• Use algebraic manipulation to simplify the equation
• Check the solution for accuracy

Q: How can I practice solving mathematical equations?

A: To practice solving mathematical equations, you can:

• Work on practice problems and exercises
• Use online resources and tools to help you solve equations
• Join a study group or find a study partner to work on equations together
• Take online courses or attend workshops to learn new skills and techniques

Conclusion

In conclusion, solving mathematical equations requires a clear understanding of the correct sequence of steps and a careful approach to algebraic manipulation. By following the correct sequence of steps and avoiding common mistakes, you can ensure that your solutions are accurate and reliable. We hope that this article has provided you with a better understanding of the missing step in a mathematical equation and has given you some valuable tips and resources to help you practice solving equations.

Discussion

The discussion category for this article is mathematics. The topic of the article is frequently asked questions related to the missing step in a mathematical equation.

Related Topics

• Mathematical equations
• Algebraic manipulation
• Problem-solving strategies
• Mathematical reasoning
• Missing step
• Correct sequence of steps
• Division by coefficient
• Solving for x

Keywords

• Mathematical equations
• Algebraic manipulation
• Problem-solving strategies
• Mathematical reasoning
• Missing step
• Correct sequence of steps
• Division by coefficient
• Solving for x
• Practice problems
• Online resources
• Study groups
• Online courses
• Workshops