Solve The Inequality N − 3 8 \textgreater − 2 5 N - \frac{3}{8} \ \textgreater \ -\frac{2}{5} N − 8 3 ​ \textgreater − 5 2 ​ For N N N .A. N \textgreater − 31 40 N \ \textgreater \ -\frac{31}{40} N \textgreater − 40 31 ​ B. N \textgreater − 1 40 N \ \textgreater \ -\frac{1}{40} N \textgreater − 40 1 ​ C. N \textless 1 40 N \ \textless \ \frac{1}{40} N \textless 40 1 ​ D. $n \

Introduction

In this article, we will focus on solving the given inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$. This involves isolating the variable $n$ and determining the range of values that satisfy the inequality. We will use basic algebraic operations and properties of inequalities to solve this problem.

Understanding the Inequality

The given inequality is $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$. To solve this inequality, we need to isolate the variable $n$ on one side of the inequality sign. We can start by adding $\frac{3}{8}$ to both sides of the inequality.

Adding $\frac{3}{8}$ to Both Sides

When we add $\frac{3}{8}$ to both sides of the inequality, we get:

$$n - \frac{3}{8} + \frac{3}{8} \ \textgreater \ -\frac{2}{5} + \frac{3}{8}$$

Simplifying the left-hand side, we get:

$$n \ \textgreater \ -\frac{2}{5} + \frac{3}{8}$$

Evaluating the Right-Hand Side

To evaluate the right-hand side of the inequality, we need to find a common denominator for the fractions. The least common multiple of $5$ and $8$ is $40$. We can rewrite the fractions with a common denominator of $40$:

$$-\frac{2}{5} = -\frac{2 \times 8}{5 \times 8} = -\frac{16}{40}$$

$$\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}$$

Now, we can add the fractions:

$$-\frac{16}{40} + \frac{15}{40} = -\frac{1}{40}$$

Simplifying the Inequality

Substituting the evaluated right-hand side back into the inequality, we get:

$$n \ \textgreater \ -\frac{1}{40}$$

Conclusion

In this article, we solved the inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$. We added $\frac{3}{8}$ to both sides of the inequality and evaluated the right-hand side to get the final solution. The solution to the inequality is $n \ \textgreater \ -\frac{1}{40}$.

Final Answer

The final answer to the inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$ is:

• $n \ \textgreater \ -\frac{1}{40}$

This is the correct solution to the inequality.

Introduction

In our previous article, we solved the inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$. We added $\frac{3}{8}$ to both sides of the inequality and evaluated the right-hand side to get the final solution. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on solving inequalities.

Q&A

Q1: What is the first step in solving the inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$?

A1: The first step in solving the inequality is to add $\frac{3}{8}$ to both sides of the inequality. This will help us isolate the variable $n$ on one side of the inequality sign.

Q2: How do we evaluate the right-hand side of the inequality?

A2: To evaluate the right-hand side of the inequality, we need to find a common denominator for the fractions. The least common multiple of $5$ and $8$ is $40$. We can rewrite the fractions with a common denominator of $40$ and then add them.

Q3: What is the final solution to the inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$?

A3: The final solution to the inequality is $n \ \textgreater \ -\frac{1}{40}$.

Q4: Can we use other methods to solve the inequality?

A4: Yes, we can use other methods to solve the inequality. For example, we can multiply both sides of the inequality by a positive number to eliminate the fraction. However, we need to be careful not to change the direction of the inequality sign.

Q5: How do we know which direction to change the inequality sign?

A5: When we multiply or divide both sides of an inequality by a negative number, we need to change the direction of the inequality sign. However, when we multiply or divide both sides of an inequality by a positive number, we do not need to change the direction of the inequality sign.

Q6: Can we solve inequalities with variables on both sides?

A6: Yes, we can solve inequalities with variables on both sides. We can use the same methods as solving linear equations, such as adding or subtracting the same value to both sides of the inequality.

Q7: How do we know if an inequality is true or false?

A7: To determine if an inequality is true or false, we can plug in a value for the variable and check if the inequality is satisfied. If the inequality is satisfied, then it is true. If the inequality is not satisfied, then it is false.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on solving inequalities. We discussed the first step in solving the inequality, evaluating the right-hand side, and the final solution. We also answered questions on using other methods to solve the inequality, changing the direction of the inequality sign, and solving inequalities with variables on both sides.

Final Answer

The final answer to the inequality $n - \frac{3}{8} \ \textgreater \ -\frac{2}{5}$ for $n$ is:

• $n \ \textgreater \ -\frac{1}{40}$

This is the correct solution to the inequality.