Solve For $h$.$\frac{h}{-40}\ \textless \ 20$Write The Solution As An Inequality (for Example, $h\ \textgreater \ 9$). $\square$

Introduction

In mathematics, inequalities are a fundamental concept that helps us compare values and solve problems. In this article, we will focus on solving linear inequalities, specifically the inequality $\frac{h}{-40} < 20$. We will break down the solution step by step and provide a clear explanation of each step.

Understanding the Inequality

The given inequality is $\frac{h}{-40} < 20$. To solve this inequality, we need to isolate the variable $h$. The first step is to multiply both sides of the inequality by $-40$. However, when we multiply or divide both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign.

Multiplying Both Sides by -40

When we multiply both sides of the inequality by $-40$, we get:

$$h > -40(20)$$

Simplifying the Right-Hand Side

Now, let's simplify the right-hand side of the inequality:

$$h > -800$$

Writing the Solution as an Inequality

The solution to the inequality is $h > -800$. This means that the value of $h$ must be greater than $-800$.

Conclusion

In this article, we solved the inequality $\frac{h}{-40} < 20$ by multiplying both sides by $-40$ and reversing the direction of the inequality sign. We then simplified the right-hand side and wrote the solution as an inequality. The solution is $h > -800$, which means that the value of $h$ must be greater than $-800$.

Tips and Tricks

• When solving inequalities, always remember to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number.
• Make sure to simplify the right-hand side of the inequality to get the final solution.
• Practice solving inequalities with different variables and coefficients to become more comfortable with the process.

Common Mistakes to Avoid

• Not reversing the direction of the inequality sign when multiplying or dividing both sides by a negative number.
• Not simplifying the right-hand side of the inequality.
• Not writing the solution as an inequality.

Real-World Applications

Solving inequalities has many real-world applications, such as:

• Finance: Inequality equations are used to calculate interest rates and investment returns.
• Science: Inequality equations are used to model population growth and decay.
• Engineering: Inequality equations are used to design and optimize systems.

Final Thoughts

Solving inequalities is an essential skill in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve linear inequalities with ease. Remember to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number, simplify the right-hand side, and write the solution as an inequality. With practice and patience, you will become proficient in solving inequalities and apply them to real-world problems.

Additional Resources

For more information on solving inequalities, check out the following resources:

• Khan Academy: Solving Linear Inequalities
• Mathway: Solving Inequalities
• Wolfram Alpha: Solving Inequalities

Conclusion

Introduction

In our previous article, we discussed how to solve linear inequalities, specifically the inequality $\frac{h}{-40} < 20$. We broke down the solution step by step and provided a clear explanation of each step. In this article, we will answer some 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 $ax + b < c$ or $ax + b > c$, where $a$, $b$, and $c$ are constants and $x$ is the variable. A quadratic inequality, on the other hand, is an inequality that can be written in the form $ax^2 + bx + c < 0$ or $ax^2 + bx + c > 0$, where $a$, $b$, and $c$ are constants and $x$ is the variable.

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 or a graph 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 inequality symbol, such as {{content}}lt; $ or {{content}}gt; $. A non-strict inequality, on the other hand, is an inequality that is written with a non-strict inequality symbol, such as $\leq$ or $\geq$.

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 coordinate plane.
2. Find the intersection of the two graphs.
3. Determine the intervals where the system is true.

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

A: A linear inequality is an inequality that can be written in the form $ax + b < c$ or $ax + b > c$, where $a$, $b$, and $c$ are constants and $x$ is the variable. A nonlinear inequality, on the other hand, is an inequality that cannot be written in this form.

Q: How do I solve a nonlinear inequality?

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

1. Graph the nonlinear function.
2. Determine the intervals where the inequality is true.
3. Use a number line or a graph to determine the solution.

Common Mistakes to Avoid

• Not reversing the direction of the inequality sign when multiplying or dividing both sides by a negative number.
• Not simplifying the right-hand side of the inequality.
• Not writing the solution as an inequality.

Real-World Applications

Solving inequalities has many real-world applications, such as:

• Finance: Inequality equations are used to calculate interest rates and investment returns.
• Science: Inequality equations are used to model population growth and decay.
• Engineering: Inequality equations are used to design and optimize systems.

Final Thoughts

Solving inequalities is an essential skill in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve linear inequalities with ease. Remember to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number, simplify the right-hand side, and write the solution as an inequality. With practice and patience, you will become proficient in solving inequalities and apply them to real-world problems.

Additional Resources

For more information on solving inequalities, check out the following resources:

• Khan Academy: Solving Linear Inequalities
• Mathway: Solving Inequalities
• Wolfram Alpha: Solving Inequalities

Conclusion

In conclusion, solving inequalities is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve linear inequalities with ease. Remember to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number, simplify the right-hand side, and write the solution as an inequality. With practice and patience, you will become proficient in solving inequalities and apply them to real-world problems.