Solve The Inequality: 2 A + 4 \textgreater 12 2a + 4 \ \textgreater \ 12 2 A + 4 \textgreater 12 Choose The Correct Solution Set:A. { A ∣ A \textgreater 2 } \{a \mid A \ \textgreater \ 2\} { A ∣ A \textgreater 2 } B. { A ∣ A \textgreater 4 } \{a \mid A \ \textgreater \ 4\} { A ∣ A \textgreater 4 } C. { A ∣ A \textgreater 8 } \{a \mid A \ \textgreater \ 8\} { A ∣ A \textgreater 8 } D. ${a

Introduction

In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. A linear inequality is an inequality that can be written in the form of a linear equation, but with an inequality symbol instead of an equal sign. In this article, we will focus on solving the inequality $2a + 4 > 12$ and choose the correct solution set from the given options.

Understanding the Inequality

The given inequality is $2a + 4 > 12$. To solve this inequality, we need to isolate the variable $a$ on one side of the inequality symbol. We can start by subtracting 4 from both sides of the inequality.

2a + 4 - 4 > 12 - 4

This simplifies to:

2a > 8

Solving for $a$

Now that we have the inequality $2a > 8$, we can solve for $a$ by dividing both sides of the inequality by 2.

\frac{2a}{2} > \frac{8}{2}

This simplifies to:

a > 4

Choosing the Correct Solution Set

Now that we have solved the inequality, we need to choose the correct solution set from the given options. The solution set is the set of all values of $a$ that satisfy the inequality.

The given options are:

A. $\{a \mid a > 2\}$ B. $\{a \mid a > 4\}$ C. $\{a \mid a > 8\}$ D. $\{a \mid a > 10\}$

Based on our solution, we can see that the correct solution set is:

B. $\{a \mid a > 4\}$

Conclusion

In this article, we solved the inequality $2a + 4 > 12$ and chose the correct solution set from the given options. We started by subtracting 4 from both sides of the inequality, then divided both sides by 2 to solve for $a$. The correct solution set is $\{a \mid a > 4\}$.

Tips and Tricks

When solving linear inequalities, it's essential to follow the same steps as solving linear equations. However, when dividing or multiplying both sides of the inequality by a negative number, we need to reverse the direction of the inequality symbol.

Common Mistakes to Avoid

When solving linear inequalities, some common mistakes to avoid include:

• Not following the correct order of operations
• Not reversing the direction of the inequality symbol when dividing or multiplying both sides by a negative number
• Not checking the solution set for extraneous solutions

Real-World Applications

Linear inequalities have numerous real-world applications, including:

• Modeling population growth and decline
• Determining the maximum or minimum value of a function
• Solving optimization problems

Practice Problems

To practice solving linear inequalities, try the following problems:

• Solve the inequality $3x - 2 > 5$
• Solve the inequality $2y + 1 < 7$
• Solve the inequality $x - 4 > 2$

Conclusion

Introduction

In our previous article, we discussed solving linear inequalities and chose the correct solution set from the given options. In this article, we will provide a Q&A guide to help you better understand and solve linear inequalities.

Q: What is a linear inequality?

A: A linear inequality is an inequality that can be written in the form of a linear equation, but with an inequality symbol instead of an equal sign.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable on one side of the inequality symbol. 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 difference between a linear inequality and a linear equation?

A: The main difference between a linear inequality and a linear equation is the inequality symbol. A linear equation has an equal sign (=), while a linear inequality has an inequality symbol (>, <, ≥, or ≤).

Q: How do I choose the correct solution set?

A: To choose the correct solution set, you need to look at the inequality symbol and determine the direction of the inequality. If the inequality symbol is (>, ≥), the solution set will be all values greater than or equal to the constant term. If the inequality symbol is (<, ≤), the solution set will be all values less than or equal to the constant term.

Q: What is the correct order of operations when solving a linear inequality?

A: The correct order of operations when solving a linear inequality is:

1. Simplify the inequality by combining like terms.
2. Add or subtract the same value to both sides of the inequality.
3. Multiply or divide both sides of the inequality by the same non-zero value.
4. Check the solution set for extraneous solutions.

Q: How do I check for extraneous solutions?

A: To check for extraneous solutions, you need to plug the solution back into the original inequality and check if it is true. If the solution is not true, it is an extraneous solution and should be discarded.

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

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

• Not following the correct order of operations
• Not reversing the direction of the inequality symbol when dividing or multiplying both sides by a negative number
• Not checking the solution set for extraneous solutions

Q: How do I apply linear inequalities to real-world problems?

A: Linear inequalities can be applied to real-world problems in a variety of ways, including:

• Modeling population growth and decline
• Determining the maximum or minimum value of a function
• Solving optimization problems

Q: What are some examples of linear inequalities in real-world problems?

A: Some examples of linear inequalities in real-world problems include:

• A company wants to determine the maximum number of employees it can hire without exceeding its budget. The inequality might be x ≤ 100, where x is the number of employees.
• A farmer wants to determine the minimum amount of water it needs to irrigate its crops. The inequality might be x ≥ 50, where x is the amount of water needed.
• A city wants to determine the maximum speed limit it can set without exceeding the safety limit. The inequality might be x ≤ 60, where x is the speed limit.

Conclusion

In conclusion, solving linear inequalities is a crucial concept in mathematics that has numerous real-world applications. By following the correct steps and avoiding common mistakes, we can solve linear inequalities with ease. Remember to practice regularly to become proficient in solving linear inequalities.