Solve For $m$.$\[ \frac{m}{5} \ \textgreater \ -50 \\]

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Introduction

In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. An inequality is a statement that compares two expressions, indicating that one is greater than, less than, or equal to the other. In this article, we will focus on solving inequalities, specifically the inequality $\frac{m}{5} > -50$. We will break down the solution step by step, providing a clear understanding of the concept and the necessary steps to find the value of $m$.

Understanding the Inequality

The given inequality is $\frac{m}{5} > -50$. To solve this inequality, we need to isolate the variable $m$ on one side of the inequality sign. The first step is to multiply both sides of the inequality by 5, which is the denominator of the fraction. This will eliminate the fraction and make it easier to solve for $m$.

Multiplying Both Sides of the Inequality

When we multiply both sides of the inequality by 5, we get:

$$m > -250$$

This is because multiplying both sides of an inequality by a positive number (in this case, 5) does not change the direction of the inequality sign.

Solving for $m$

Now that we have the inequality $m > -250$, we can see that $m$ is greater than -250. This means that any value of $m$ that is greater than -250 will satisfy the inequality.

Example Solutions

To illustrate this, let's consider some example solutions:

• $m = -249$ satisfies the inequality because it is greater than -250.
• $m = -251$ does not satisfy the inequality because it is less than -250.
• $m = 0$ satisfies the inequality because it is greater than -250.

Conclusion

In conclusion, solving inequalities involves isolating the variable on one side of the inequality sign and then determining the range of values that satisfy the inequality. In this article, we solved the inequality $\frac{m}{5} > -50$ by multiplying both sides by 5 and then determining the range of values that satisfy the inequality. We hope that this article has provided a clear understanding of the concept and the necessary steps to solve inequalities.

Tips and Tricks

Here are some tips and tricks to keep in mind when solving inequalities:

• Always multiply both sides of the inequality by the same number to avoid changing the direction of the inequality sign.
• Be careful when multiplying both sides of the inequality by a negative number, as this will change the direction of the inequality sign.
• Use a number line to visualize the solution to the inequality and determine the range of values that satisfy the inequality.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving inequalities:

• Not multiplying both sides of the inequality by the same number.
• Changing the direction of the inequality sign when multiplying both sides by a negative number.
• Not considering the range of values that satisfy the inequality.

Real-World Applications

Inequalities have many real-world applications, including:

• Finance: Inequalities are used to calculate interest rates and investment returns.
• 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 an essential skill in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve inequalities with confidence and accuracy. Remember to always multiply both sides of the inequality by the same number, be careful when multiplying both sides by a negative number, and use a number line to visualize the solution to the inequality. With practice and patience, you can become proficient in solving inequalities and apply this skill to real-world problems.

Additional Resources

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

Final Thoughts

Introduction

In our previous article, we discussed the concept of solving inequalities and provided a step-by-step guide to finding the value of $m$ in the inequality $\frac{m}{5} > -50$. In this article, we will answer some frequently asked questions about solving inequalities, providing additional insights and examples to help you master this essential math skill.

Q: What is the difference between an inequality and an equation?

A: An equation is a statement that says two expressions are equal, while an inequality is a statement that says one expression is greater than, less than, or equal to another expression.

Q: How do I solve an inequality with a variable on both sides?

A: To solve an inequality with a variable on both sides, you need to isolate the variable on one side of the inequality sign. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.

Q: What is the rule for multiplying or dividing both sides of an inequality by a negative number?

A: When you multiply or divide both sides of an inequality by a negative number, you need to change the direction of the inequality sign. For example, if you have the inequality $x > 5$ and you multiply both sides by -1, the resulting inequality would be $-x < -5$.

Q: How do I determine the solution to an inequality?

A: To determine the solution to an inequality, you need to find the values of the variable that make the inequality true. You can do this by using a number line or by testing different values of the variable.

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. A quadratic inequality 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.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you need to factor the quadratic expression and then use the sign of the expression to determine the solution. You can also use the quadratic formula to find the roots of the quadratic expression and then use a number line to determine the solution.

Q: What is the importance of solving inequalities in real-world applications?

A: Solving inequalities is an essential skill in mathematics that has many real-world applications. Inequalities are used to model population growth and decay, to calculate interest rates and investment returns, and to design and optimize systems.

Q: How can I practice solving inequalities?

A: You can practice solving inequalities by working through examples and exercises in a math textbook or online resource. You can also use online tools and calculators to help you solve inequalities.

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

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

• Not multiplying both sides of the inequality by the same number
• Changing the direction of the inequality sign when multiplying both sides by a negative number
• Not considering the range of values that satisfy the inequality

Conclusion

In conclusion, solving inequalities is an essential skill in mathematics that has many real-world applications. By following the steps outlined in this article and practicing with examples and exercises, you can master this skill and apply it to real-world problems. Remember to always multiply both sides of the inequality by the same number, be careful when multiplying both sides by a negative number, and use a number line to visualize the solution to the inequality.

Additional Resources

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

Final Thoughts

Solving inequalities is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article and practicing with examples and exercises, you can master this skill and apply it to real-world problems. Remember to always multiply both sides of the inequality by the same number, be careful when multiplying both sides by a negative number, and use a number line to visualize the solution to the inequality. With practice and patience, you can become proficient in solving inequalities and apply this skill to real-world problems.