Solve For $a$.$\frac{a}{-3} \geq 50$Write The Solution As An Inequality (for Example, $a\ \textgreater \ 9$). $\square$

Introduction

In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. An inequality is a statement that two expressions are not equal, but one is greater than or less than the other. In this article, we will focus on solving inequalities, specifically the inequality $\frac{a}{-3} \geq 50$. We will walk you through the step-by-step process of isolating the variable $a$ and provide a clear understanding of the solution.

Understanding the Inequality

The given inequality is $\frac{a}{-3} \geq 50$. To solve this inequality, we need to isolate the variable $a$. The first step is to understand the inequality and identify the operations that need to be performed to isolate the variable.

Multiplying Both Sides by -3

To isolate the variable $a$, we need to get rid of the fraction. We can do this by multiplying both sides of the inequality by $-3$. 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.

\frac{a}{-3} \geq 50
\implies a \leq -150

Isolating the Variable

Now that we have multiplied both sides of the inequality by $-3$, we have isolated the variable $a$. The inequality is now in the form $a \leq -150$. This means that the value of $a$ is less than or equal to $-150$.

Solution as an Inequality

The solution to the inequality $\frac{a}{-3} \geq 50$ is $a \leq -150$. This can be written as an inequality in the form $a \leq -150$.

Conclusion

In this article, we have solved the inequality $\frac{a}{-3} \geq 50$ by isolating the variable $a$. We have walked you through the step-by-step process of multiplying both sides of the inequality by $-3$ and reversing the direction of the inequality sign. The solution to the inequality is $a \leq -150$, which can be written as an inequality in the form $a \leq -150$.

Frequently Asked Questions

• What is an inequality?
• How do I solve an inequality?
• What is the solution to the inequality $\frac{a}{-3} \geq 50$?

Answering Frequently Asked Questions

• What is an inequality?

  An inequality is a statement that two expressions are not equal, but one is greater than or less than the other.

• How do I solve an inequality?

  To solve an inequality, you need to isolate the variable by performing the necessary operations to get rid of the fraction or other obstacles.

• What is the solution to the inequality $\frac{a}{-3} \geq 50$?

  The solution to the inequality $\frac{a}{-3} \geq 50$ is $a \leq -150$.

Tips and Tricks

• When solving an inequality, make sure to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number.
• Use the correct operations to isolate the variable and get rid of the fraction or other obstacles.
• Write the solution as an inequality in the form $a \leq -150$.

Real-World Applications

Inequalities are used in various real-world applications, such as:

• Finance: Inequalities are used to calculate interest rates and investments.
• Science: Inequalities are used to model population growth and decay.
• Engineering: Inequalities are used to design and optimize systems.

Conclusion

In conclusion, solving inequalities is a crucial concept in mathematics that has various real-world applications. By following the step-by-step process outlined in this article, you can solve inequalities and isolate the variable. Remember to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number and write the solution as an inequality in the form $a \leq -150$.

Introduction

In our previous article, we discussed how to solve inequalities by isolating the variable. In this article, we will provide a Q&A guide to help you understand the concept of solving inequalities better. We will cover various questions and answers related to solving inequalities, including tips and tricks, real-world applications, and more.

Q&A Guide

Q1: What is an inequality?

A1: An inequality is a statement that two expressions are not equal, but one is greater than or less than the other.

Q2: How do I solve an inequality?

A2: To solve an inequality, you need to isolate the variable by performing the necessary operations to get rid of the fraction or other obstacles.

Q3: What is the solution to the inequality $\frac{a}{-3} \geq 50$?

A3: The solution to the inequality $\frac{a}{-3} \geq 50$ is $a \leq -150$.

Q4: When should I reverse the direction of the inequality sign?

A4: You should reverse the direction of the inequality sign when multiplying or dividing both sides of the inequality by a negative number.

Q5: How do I write the solution as an inequality?

A5: You should write the solution as an inequality in the form $a \leq -150$.

Q6: What are some real-world applications of inequalities?

A6: Inequalities are used in various real-world applications, such as finance, science, and engineering.

Q7: How do I use inequalities to model population growth and decay?

A7: You can use inequalities to model population growth and decay by setting up an inequality that represents the rate of change of the population.

Q8: How do I use inequalities to design and optimize systems?

A8: You can use inequalities to design and optimize systems by setting up an inequality that represents the constraints of the system.

Q9: What are some tips and tricks for solving inequalities?

A9: Some tips and tricks for solving inequalities include:

• Reversing the direction of the inequality sign when multiplying or dividing both sides by a negative number.
• Using the correct operations to isolate the variable and get rid of the fraction or other obstacles.
• Writing the solution as an inequality in the form $a \leq -150$.

Q10: How do I check my solution to an inequality?

A10: You can check your solution to an inequality by plugging in a value for the variable and checking if the inequality holds true.

Conclusion

In conclusion, solving inequalities is a crucial concept in mathematics that has various real-world applications. By following the step-by-step process outlined in this article and using the tips and tricks provided, you can solve inequalities and isolate the variable. Remember to reverse the direction of the inequality sign when multiplying or dividing both sides by a negative number and write the solution as an inequality in the form $a \leq -150$.