Solve The Inequality: − 1 2 A \textgreater 10 \frac{-1}{2} A \ \textgreater \ 10 2 − 1 ​ A \textgreater 10 Enter The Correct Answer: □ □ □ 10 \frac{\square \square}{\square 10} □ 10 □□ ​

Introduction

In mathematics, inequalities are a fundamental concept that deals with the comparison of two or more mathematical expressions. They are used to describe the relationship between different quantities, and solving inequalities is an essential skill in mathematics. In this article, we will focus on solving the inequality $\frac{-1}{2} a \ \textgreater \ 10$ and provide a step-by-step guide on how to solve it.

Understanding the Inequality

The given inequality is $\frac{-1}{2} a \ \textgreater \ 10$. To solve this inequality, we need to isolate the variable $a$ on one side of the inequality sign. The inequality sign $\textgreater$ indicates that the value of $a$ is greater than the value on the other side of the inequality sign.

Step 1: Multiply Both Sides by -1

To isolate the variable $a$, we need to get rid of the fraction on the left-hand side of the inequality. We can do this by multiplying both sides of the inequality by $-1$. However, when we multiply both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign.

\frac{-1}{2} a \  \textgreater \  10
\Rightarrow \  -\frac{1}{2} a \  \textless \  -10

Step 2: Multiply Both Sides by -2

To get rid of the fraction on the left-hand side of the inequality, we can multiply both sides of the inequality by $-2$. This will eliminate the fraction and allow us to isolate the variable $a$.

-\frac{1}{2} a \  \textless \  -10
\Rightarrow \  a \  \textless \  20

Step 3: Write the Solution in the Required Format

The solution to the inequality is $a \ \textless \ 20$. However, the problem requires us to write the solution in the format $\frac{\square \square}{\square 10}$. To do this, we need to rewrite the solution in the required format.

Conclusion

In this article, we solved the inequality $\frac{-1}{2} a \ \textgreater \ 10$ and provided a step-by-step guide on how to solve it. We multiplied both sides of the inequality by $-1$ and then by $-2$ to isolate the variable $a$. Finally, we wrote the solution in the required format $\frac{\square \square}{\square 10}$. The solution to the inequality is $a \ \textless \ 20$, which can be written in the required format as $\frac{\square \square}{\square 10}$.

Final Answer

The final answer is $\boxed{\frac{\square \square}{\square 10}}$.

Introduction

In our previous article, we solved the inequality $\frac{-1}{2} a \ \textgreater \ 10$ and provided a step-by-step guide on how to solve it. In this article, we will answer some of the most frequently asked questions related to solving inequalities.

Q&A

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two or more expressions. It is used to describe the relationship between different quantities.

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

A: An equation is a mathematical statement that states that two or more expressions are equal. An inequality, on the other hand, states that two or more expressions are not equal, but rather one is greater than, less than, or equal to the other.

Q: How do I solve an inequality?

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

Q: What is the order of operations for solving inequalities?

A: The order of operations for solving inequalities is the same as for solving equations:

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I handle negative numbers when solving inequalities?

A: When solving inequalities, you need to be careful when handling negative numbers. If you multiply or divide both sides of the inequality by a negative number, you need to reverse the direction of the inequality sign.

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 sign, such as $a \ \textgreater \ b$ or $a \ \textless \ b$. A non-strict inequality is an inequality that is written with a non-strict inequality sign, such as $a \ \geq \ b$ or $a \ \leq \ b$.

Q: How do I write the solution to an inequality in the required format?

A: To write the solution to an inequality in the required format, you need to isolate the variable on one side of the inequality sign and then rewrite the solution in the required format.

Conclusion

In this article, we answered some of the most frequently asked questions related to solving inequalities. We covered topics such as the definition of an inequality, the difference between an inequality and an equation, and the order of operations for solving inequalities. We also discussed how to handle negative numbers and the difference between strict and non-strict inequalities.

Final Answer

The final answer is $\boxed{\frac{\square \square}{\square 10}}$.