Solve For $n$. $-500 \ \textgreater \ -5n$ Write The Solution As An Inequality (for Example, \$n \ \textgreater \ 9$[/tex\]). $\square$

by ADMIN 148 views

Introduction

In mathematics, solving inequalities is a crucial skill that helps us understand the relationships between variables and make informed decisions. In this article, we will focus on solving a specific inequality, $-500 \ \textgreater \ -5n$, and provide a step-by-step guide to finding the solution.

Understanding the Inequality

Before we dive into solving the inequality, let's understand what it means. The inequality $-500 \ \textgreater \ -5n$ states that the value of $-500$ is greater than the value of $-5n$. In other words, we are looking for the values of $n$ that make the inequality true.

Step 1: Isolate the Variable

To solve the inequality, we need to isolate the variable $n$. We can do this by adding $5n$ to both sides of the inequality, which gives us:

−500+5n \textgreater 0-500 + 5n \ \textgreater \ 0

Step 2: Simplify the Inequality

Now that we have isolated the variable, we can simplify the inequality by combining like terms. In this case, we can add $500$ to both sides of the inequality, which gives us:

5n \textgreater 5005n \ \textgreater \ 500

Step 3: Solve for $n$

To solve for $n$, we need to divide both sides of the inequality by $5$. This gives us:

n \textgreater 100n \ \textgreater \ 100

Conclusion

In conclusion, the solution to the inequality $-500 \ \textgreater \ -5n$ is $n \ \textgreater \ 100$. This means that any value of $n$ greater than $100$ will make the inequality true.

Real-World Applications

Solving inequalities has many real-world applications, including:

  • Finance: In finance, inequalities are used to model the relationships between variables such as interest rates, stock prices, and investment returns.
  • Science: In science, inequalities are used to model the relationships between variables such as temperature, pressure, and volume.
  • Engineering: In engineering, inequalities are used to model the relationships between variables such as stress, strain, and material properties.

Tips and Tricks

Here are some tips and tricks to help you solve inequalities:

  • Use inverse operations: To solve an inequality, you can use inverse operations such as addition, subtraction, multiplication, and division.
  • Watch your signs: When solving an inequality, make sure to watch your signs and keep track of the direction of the inequality.
  • Use a number line: A number line can be a helpful tool when solving inequalities, as it allows you to visualize the relationships between variables.

Common Mistakes

Here are some common mistakes to avoid when solving inequalities:

  • Not isolating the variable: Make sure to isolate the variable on one side of the inequality.
  • Not simplifying the inequality: Make sure to simplify the inequality by combining like terms.
  • Not checking your solution: Make sure to check your solution by plugging it back into the original inequality.

Conclusion

In conclusion, solving inequalities is a crucial skill that helps us understand the relationships between variables and make informed decisions. By following the steps outlined in this article, you can solve inequalities with confidence and accuracy. Remember to use inverse operations, watch your signs, and use a number line to help you visualize the relationships between variables. With practice and patience, you will become a master of solving inequalities in no time!

Introduction

In our previous article, we provided a step-by-step guide to solving the inequality $-500 \ \textgreater \ -5n$. In this article, we will answer some of the most frequently asked questions about solving inequalities.

Q&A

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that can be written in the form $ax + b \ \textgreater \ c$, where $a$, $b$, and $c$ are constants. A quadratic inequality, on the other hand, is an inequality that can be written in the form $ax^2 + bx + c \ \textgreater \ 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you can use the following steps:

  1. Factor the quadratic expression, if possible.
  2. Set each factor equal to zero and solve for the variable.
  3. Use a number line to determine the intervals where the inequality is true.

Q: What is the difference between a strict inequality and a non-strict inequality?

A: A strict inequality is an inequality that is written with a strict symbol, such as $\ \textgreater \ $ or $\ \textless \ $. A non-strict inequality, on the other hand, is an inequality that is written with a non-strict symbol, such as $\ \geq \ $ or $\ \leq \ $.

Q: How do I solve a system of linear inequalities?

A: To solve a system of linear inequalities, you can use the following steps:

  1. Graph each inequality on a number line.
  2. Find the intersection of the two number lines.
  3. Determine the intervals where the system of inequalities is true.

Q: What is the difference between a linear programming problem and a quadratic programming problem?

A: A linear programming problem is a problem that involves maximizing or minimizing a linear function subject to a set of linear constraints. A quadratic programming problem, on the other hand, is a problem that involves maximizing or minimizing a quadratic function subject to a set of linear constraints.

Q: How do I solve a linear programming problem?

A: To solve a linear programming problem, you can use the following steps:

  1. Write the objective function and the constraints.
  2. Graph the feasible region.
  3. Find the optimal solution by evaluating the objective function at the vertices of the feasible region.

Q: What is the difference between a maximization problem and a minimization problem?

A: A maximization problem is a problem that involves maximizing a function subject to a set of constraints. A minimization problem, on the other hand, is a problem that involves minimizing a function subject to a set of constraints.

Q: How do I solve a maximization problem?

A: To solve a maximization problem, you can use the following steps:

  1. Write the objective function and the constraints.
  2. Graph the feasible region.
  3. Find the optimal solution by evaluating the objective function at the vertices of the feasible region.

Conclusion

In conclusion, solving inequalities is a crucial skill that helps us understand the relationships between variables and make informed decisions. By following the steps outlined in this article, you can answer some of the most frequently asked questions about solving inequalities. Remember to use inverse operations, watch your signs, and use a number line to help you visualize the relationships between variables. With practice and patience, you will become a master of solving inequalities in no time!

Additional Resources

  • Inequality Solver: A online tool that helps you solve inequalities.
  • Mathway: A online tool that helps you solve math problems, including inequalities.
  • Khan Academy: A online resource that provides video lessons and practice exercises on solving inequalities.

Final Tips

  • Practice, practice, practice: The more you practice solving inequalities, the more confident you will become.
  • Use a number line: A number line can be a helpful tool when solving inequalities, as it allows you to visualize the relationships between variables.
  • Check your solution: Make sure to check your solution by plugging it back into the original inequality.