Solve The Inequality:${ -8x \ \textless \ 80 }$

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Introduction

In this article, we will focus on solving the given inequality, $-8x < 80$. Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to. Solving an inequality involves finding the values of the variable that make the inequality true. In this case, we need to isolate the variable $x$ and find its possible values.

Understanding the Inequality

The given inequality is $-8x < 80$. This means that the product of $-8$ and $x$ is less than $80$. To solve this inequality, we need to isolate the variable $x$.

Isolating the Variable

To isolate the variable $x$, we need to get rid of the coefficient $-8$. We can do this by dividing both sides of the inequality by $-8$. However, when we divide by a negative number, we need to reverse the direction of the inequality.

Solving the Inequality

To solve the inequality, we need to divide both sides by $-8$ and reverse the direction of the inequality.

$$-8x < 80$$

$$\frac{-8x}{-8} > \frac{80}{-8}$$

$$x > -10$$

Conclusion

In this article, we solved the inequality $-8x < 80$. We isolated the variable $x$ by dividing both sides of the inequality by $-8$ and reversing the direction of the inequality. The solution to the inequality is $x > -10$. This means that any value of $x$ that is greater than $-10$ will make the inequality true.

Examples and Applications

Here are a few examples and applications of solving the inequality $-8x < 80$:

• If we have a box with a length of $x$ meters, and the box can hold a maximum of $80$ kilograms of weight, then the length of the box must be greater than $-10$ meters.
• If we have a bank account with a balance of $x$ dollars, and the account can earn a maximum of $80$ dollars per month, then the balance in the account must be greater than $-10$ dollars.
• If we have a temperature reading of $x$ degrees Celsius, and the temperature can drop to a minimum of $-10$ degrees Celsius, then the temperature reading must be greater than $-10$ degrees Celsius.

Tips and Tricks

Here are a few tips and tricks for solving inequalities:

• When dividing by a negative number, reverse the direction of the inequality.
• When multiplying or dividing both sides of an inequality by a negative number, reverse the direction of the inequality.
• When adding or subtracting both sides of an inequality by a positive number, the direction of the inequality remains the same.
• When adding or subtracting both sides of an inequality by a negative number, the direction of the inequality remains the same.

Common Mistakes

Here are a few common mistakes to avoid when solving inequalities:

• Not reversing the direction of the inequality when dividing by a negative number.
• Not isolating the variable on one side of the inequality.
• Not checking the solution to the inequality.
• Not considering the domain of the variable.

Conclusion

In this article, we solved the inequality $-8x < 80$. We isolated the variable $x$ by dividing both sides of the inequality by $-8$ and reversing the direction of the inequality. The solution to the inequality is $x > -10$. This means that any value of $x$ that is greater than $-10$ will make the inequality true. We also discussed examples and applications of solving the inequality, and provided tips and tricks for solving inequalities. Finally, we discussed common mistakes to avoid when solving inequalities.

Final Answer

The final answer is $\boxed{x > -10}$.

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Introduction

In our previous article, we solved the inequality $-8x < 80$. In this article, we will answer some frequently asked questions about solving inequalities, with a focus on the inequality $-8x < 80$.

Q1: What is the solution to the inequality $-8x < 80$?

A1: The solution to the inequality $-8x < 80$ is $x > -10$. This means that any value of $x$ that is greater than $-10$ will make the inequality true.

Q2: How do I isolate the variable $x$ in the inequality $-8x < 80$?

A2: To isolate the variable $x$, you need to get rid of the coefficient $-8$. You can do this by dividing both sides of the inequality by $-8$. However, when you divide by a negative number, you need to reverse the direction of the inequality.

Q3: What happens when I divide both sides of the inequality by a negative number?

A3: When you divide both sides of the inequality by a negative number, you need to reverse the direction of the inequality. For example, if you have the inequality $-8x < 80$, and you divide both sides by $-8$, the inequality becomes $x > -10$.

Q4: Can I add or subtract both sides of the inequality by a negative number?

A4: Yes, you can add or subtract both sides of the inequality by a negative number. However, you need to reverse the direction of the inequality. For example, if you have the inequality $-8x < 80$, and you add $20$ to both sides, the inequality becomes $-8x + 20 < 100$.

Q5: What is the domain of the variable $x$ in the inequality $-8x < 80$?

A5: The domain of the variable $x$ in the inequality $-8x < 80$ is all real numbers. This means that $x$ can take on any value, as long as it is greater than $-10$.

Q6: Can I use the inequality $-8x < 80$ to solve a real-world problem?

A6: Yes, you can use the inequality $-8x < 80$ to solve a real-world problem. For example, if you have a box with a length of $x$ meters, and the box can hold a maximum of $80$ kilograms of weight, then the length of the box must be greater than $-10$ meters.

Q7: What are some common mistakes to avoid when solving inequalities?

A7: Some common mistakes to avoid when solving inequalities include:

• Not reversing the direction of the inequality when dividing by a negative number.
• Not isolating the variable on one side of the inequality.
• Not checking the solution to the inequality.
• Not considering the domain of the variable.

Q8: How do I check the solution to the inequality $-8x < 80$?

A8: To check the solution to the inequality $-8x < 80$, you need to plug in a value of $x$ that is greater than $-10$ into the inequality and see if it is true. For example, if you plug in $x = 0$, the inequality becomes $-8(0) < 80$, which is true.

Q9: Can I use the inequality $-8x < 80$ to solve a system of inequalities?

A9: Yes, you can use the inequality $-8x < 80$ to solve a system of inequalities. For example, if you have two inequalities, $-8x < 80$ and $x > 5$, you can solve the system by finding the intersection of the two inequalities.

Q10: What are some real-world applications of solving inequalities?

A10: Some real-world applications of solving inequalities include:

• Solving optimization problems, such as finding the maximum or minimum value of a function.
• Solving systems of inequalities, such as finding the intersection of two or more inequalities.
• Solving linear programming problems, such as finding the optimal solution to a linear programming problem.

Conclusion

In this article, we answered some frequently asked questions about solving inequalities, with a focus on the inequality $-8x < 80$. We discussed how to isolate the variable $x$, how to divide both sides of the inequality by a negative number, and how to check the solution to the inequality. We also discussed some common mistakes to avoid when solving inequalities and some real-world applications of solving inequalities.