What Is The Solution To The Inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?A. $x \ \textgreater \ 3$B. $x \ \textless \ 3$C. $x \ \textgreater \ -19$D. $x \ \textless \ -19$

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Introduction

Inequality is a mathematical statement that contains a variable and a constant, and the relationship between them is not equal. In this article, we will focus on solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$. This type of inequality is called a linear inequality, and it can be solved using algebraic methods.

Understanding the Inequality

The given inequality is $\frac{1}{4}(11-x) \ \textgreater \ 2$. To solve this inequality, we need to isolate the variable $x$. The first step is to multiply both sides of the inequality by 4 to eliminate the fraction.

Multiplying Both Sides by 4

Multiplying both sides of the inequality by 4 gives us:

$$\frac{1}{4}(11-x) \ \textgreater \ 2$$

$$\Rightarrow \ 11-x \ \textgreater \ 8$$

Isolating the Variable

Now, we need to isolate the variable $x$. To do this, we need to subtract 11 from both sides of the inequality.

Subtracting 11 from Both Sides

Subtracting 11 from both sides of the inequality gives us:

$$11-x \ \textgreater \ 8$$

$$\Rightarrow \ -x \ \textgreater \ -3$$

Solving for x

Now, we need to solve for $x$. To do this, we need to multiply both sides of the inequality by -1.

Multiplying Both Sides by -1

Multiplying both sides of the inequality by -1 gives us:

$$-x \ \textgreater \ -3$$

$$\Rightarrow \ x \ \textless \ 3$$

Conclusion

In conclusion, the solution to the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is $x \ \textless \ 3$. This means that any value of $x$ that is less than 3 will satisfy the inequality.

Discussion

The solution to the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is $x \ \textless \ 3$. This means that any value of $x$ that is less than 3 will satisfy the inequality. The inequality is a linear inequality, and it can be solved using algebraic methods.

Final Answer

The final answer is $x \ \textless \ 3$.

Step-by-Step Solution

Here is the step-by-step solution to the inequality:

1. Multiply both sides of the inequality by 4 to eliminate the fraction.
2. Subtract 11 from both sides of the inequality to isolate the variable $x$.
3. Multiply both sides of the inequality by -1 to solve for $x$.

Common Mistakes

Here are some common mistakes to avoid when solving the inequality:

• Not multiplying both sides of the inequality by 4 to eliminate the fraction.
• Not subtracting 11 from both sides of the inequality to isolate the variable $x$.
• Not multiplying both sides of the inequality by -1 to solve for $x$.

Real-World Applications

The inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ has many real-world applications. For example, it can be used to model the cost of producing a product, where $x$ is the number of units produced and the cost is given by the inequality.

Conclusion

In conclusion, the solution to the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is $x \ \textless \ 3$. This means that any value of $x$ that is less than 3 will satisfy the inequality. The inequality is a linear inequality, and it can be solved using algebraic methods.

Final Answer

The final answer is $x \ \textless \ 3$.

Step-by-Step Solution

Here is the step-by-step solution to the inequality:

1. Multiply both sides of the inequality by 4 to eliminate the fraction.
2. Subtract 11 from both sides of the inequality to isolate the variable $x$.
3. Multiply both sides of the inequality by -1 to solve for $x$.

Common Mistakes

Here are some common mistakes to avoid when solving the inequality:

• Not multiplying both sides of the inequality by 4 to eliminate the fraction.
• Not subtracting 11 from both sides of the inequality to isolate the variable $x$.
• Not multiplying both sides of the inequality by -1 to solve for $x$.

Real-World Applications

The inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ has many real-world applications. For example, it can be used to model the cost of producing a product, where $x$ is the number of units produced and the cost is given by the inequality.

Conclusion

In conclusion, the solution to the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is $x \ \textless \ 3$. This means that any value of $x$ that is less than 3 will satisfy the inequality. The inequality is a linear inequality, and it can be solved using algebraic methods.

Final Answer

The final answer is $x \ \textless \ 3$.

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Introduction

In our previous article, we solved the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ and found that the solution is $x \ \textless \ 3$. In this article, we will answer some frequently asked questions about solving this inequality.

Q: What is the first step in solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?

A: The first step in solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is to multiply both sides of the inequality by 4 to eliminate the fraction.

Q: Why do we need to multiply both sides of the inequality by 4?

A: We need to multiply both sides of the inequality by 4 to eliminate the fraction. This is because the fraction $\frac{1}{4}$ is not a whole number, and we want to get rid of it to make the inequality easier to solve.

Q: What is the next step in solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?

A: The next step in solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is to subtract 11 from both sides of the inequality to isolate the variable $x$.

Q: Why do we need to subtract 11 from both sides of the inequality?

A: We need to subtract 11 from both sides of the inequality to isolate the variable $x$. This is because we want to get $x$ by itself on one side of the inequality.

Q: What is the final step in solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?

A: The final step in solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is to multiply both sides of the inequality by -1 to solve for $x$.

Q: Why do we need to multiply both sides of the inequality by -1?

A: We need to multiply both sides of the inequality by -1 to solve for $x$. This is because we want to get $x$ by itself on one side of the inequality.

Q: What is the solution to the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?

A: The solution to the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ is $x \ \textless \ 3$.

Q: What are some common mistakes to avoid when solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?

A: Some common mistakes to avoid when solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ are:

• Not multiplying both sides of the inequality by 4 to eliminate the fraction.
• Not subtracting 11 from both sides of the inequality to isolate the variable $x$.
• Not multiplying both sides of the inequality by -1 to solve for $x$.

Q: What are some real-world applications of the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$?

A: Some real-world applications of the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ are:

• Modeling the cost of producing a product, where $x$ is the number of units produced and the cost is given by the inequality.
• Determining the maximum number of units that can be produced within a certain budget.

Conclusion

In conclusion, solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ requires careful attention to detail and a step-by-step approach. By following the steps outlined in this article, you can solve this inequality and apply it to real-world problems.

Final Answer

The final answer is $x \ \textless \ 3$.

Step-by-Step Solution

Here is the step-by-step solution to the inequality:

1. Multiply both sides of the inequality by 4 to eliminate the fraction.
2. Subtract 11 from both sides of the inequality to isolate the variable $x$.
3. Multiply both sides of the inequality by -1 to solve for $x$.

Common Mistakes

Here are some common mistakes to avoid when solving the inequality:

• Not multiplying both sides of the inequality by 4 to eliminate the fraction.
• Not subtracting 11 from both sides of the inequality to isolate the variable $x$.
• Not multiplying both sides of the inequality by -1 to solve for $x$.

Real-World Applications

The inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ has many real-world applications. For example, it can be used to model the cost of producing a product, where $x$ is the number of units produced and the cost is given by the inequality.

Conclusion

In conclusion, solving the inequality $\frac{1}{4}(11-x) \ \textgreater \ 2$ requires careful attention to detail and a step-by-step approach. By following the steps outlined in this article, you can solve this inequality and apply it to real-world problems.

Final Answer

The final answer is $x \ \textless \ 3$.