Solve For $d$.$\frac{2}{5} \ \textgreater \ 2d$Write The Solution As An Inequality (for Example, $d \ \textgreater \ 9$).Options:- $\ \textless \ $- $\leq$- $\geq$- $=$Graph The

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Introduction

In this problem, we are given an inequality $\frac{2}{5} \ \textgreater \ 2d$ and we need to solve for $d$. This means we need to isolate the variable $d$ on one side of the inequality. We will use basic algebraic operations to solve the inequality and express the solution as a mathematical statement.

Step 1: Multiply both sides of the inequality by 5

To get rid of the fraction, we can multiply both sides of the inequality by 5. This will give us $2 \ \textgreater \ 10d$. We can do this because multiplying or dividing both sides of an inequality by a positive number does not change the direction of the inequality.

Step 2: Divide both sides of the inequality by 10

Now, we need to isolate the variable $d$ on one side of the inequality. We can do this by dividing both sides of the inequality by 10. This will give us $\frac{1}{5} \ \textgreater \ d$. We can do this because dividing both sides of an inequality by a positive number does not change the direction of the inequality.

Step 3: Write the solution as an inequality

The solution to the inequality is $d \ \textless \ \frac{1}{5}$. This means that $d$ is less than $\frac{1}{5}$.

Step 4: Graph the solution

To graph the solution, we can draw a number line and mark the point $\frac{1}{5}$. We can then shade the region to the left of the point, indicating that $d$ is less than $\frac{1}{5}$.

Conclusion

In this problem, we solved the inequality $\frac{2}{5} \ \textgreater \ 2d$ and expressed the solution as a mathematical statement. We also graphed the solution on a number line.

Solution Options

The solution options are:

• $\ \textless \ $: This is the correct solution.
• $\leq$: This is not the correct solution because $d$ is less than $\frac{1}{5}$, not less than or equal to $\frac{1}{5}$.
• $\geq$: This is not the correct solution because $d$ is less than $\frac{1}{5}$, not greater than or equal to $\frac{1}{5}$.
• $=$: This is not the correct solution because $d$ is less than $\frac{1}{5}$, not equal to $\frac{1}{5}$.

Graphing the Solution

To graph the solution, we can draw a number line and mark the point $\frac{1}{5}$. We can then shade the region to the left of the point, indicating that $d$ is less than $\frac{1}{5}$. This is shown in the graph below:

[Insert graph here]

Discussion

This problem is a basic algebraic inequality problem. We used basic algebraic operations to solve the inequality and express the solution as a mathematical statement. We also graphed the solution on a number line. This type of problem is commonly seen in algebra and is an important concept to understand.

Importance of Solving Inequalities

Solving inequalities is an important concept in algebra and is used in many real-world applications. Inequalities are used to model real-world problems and to make decisions based on data. For example, in finance, inequalities are used to model investment returns and to make decisions about investments. In engineering, inequalities are used to model physical systems and to make decisions about design and construction.

Conclusion

In this problem, we solved the inequality $\frac{2}{5} \ \textgreater \ 2d$ and expressed the solution as a mathematical statement. We also graphed the solution on a number line. This type of problem is commonly seen in algebra and is an important concept to understand.

Final Answer

The final answer is $\boxed{d \ \textless \ \frac{1}{5}}$.

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Introduction

In this article, we will provide a Q&A section to help clarify any questions or doubts that readers may have about solving the inequality $\frac{2}{5} \ \textgreater \ 2d$. We will cover common questions and provide step-by-step explanations to help readers understand the solution.

Q: What is the first step in solving the inequality $\frac{2}{5} \ \textgreater \ 2d$?

A: The first step in solving the inequality is to multiply both sides of the inequality by 5. This will get rid of the fraction and make it easier to work with.

Q: Why can we multiply both sides of the inequality by 5?

A: We can multiply both sides of the inequality by 5 because 5 is a positive number. Multiplying or dividing both sides of an inequality by a positive number does not change the direction of the inequality.

Q: What is the next step in solving the inequality?

A: The next step in solving the inequality is to divide both sides of the inequality by 10. This will isolate the variable $d$ on one side of the inequality.

Q: Why can we divide both sides of the inequality by 10?

A: We can divide both sides of the inequality by 10 because 10 is a positive number. Dividing both sides of an inequality by a positive number does not change the direction of the inequality.

Q: What is the final step in solving the inequality?

A: The final step in solving the inequality is to write the solution as a mathematical statement. In this case, the solution is $d \ \textless \ \frac{1}{5}$.

Q: How do we graph the solution?

A: To graph the solution, we can draw a number line and mark the point $\frac{1}{5}$. We can then shade the region to the left of the point, indicating that $d$ is less than $\frac{1}{5}$.

Q: What are some common mistakes to avoid when solving inequalities?

A: Some common mistakes to avoid when solving inequalities include:

• Multiplying or dividing both sides of the inequality by a negative number, which can change the direction of the inequality.
• Forgetting to flip the inequality sign when multiplying or dividing both sides of the inequality by a negative number.
• Not checking the solution to make sure it is consistent with the original inequality.

Q: How do we check the solution to an inequality?

A: To check the solution to an inequality, we can plug in a value from the solution set into the original inequality and check if it is true. If the value satisfies the inequality, then the solution is correct.

Q: What are some real-world applications of solving inequalities?

A: Solving inequalities has many real-world applications, including:

• Modeling investment returns in finance
• Modeling physical systems in engineering
• Making decisions based on data in business and economics

Conclusion

In this Q&A article, we have provided answers to common questions about solving the inequality $\frac{2}{5} \ \textgreater \ 2d$. We have covered the steps involved in solving the inequality, as well as common mistakes to avoid and real-world applications of solving inequalities.

Final Answer

The final answer is $\boxed{d \ \textless \ \frac{1}{5}}$.