Solve The Inequality. X − 7 \textgreater − 3.1 X - 7 \ \textgreater \ -3.1 X − 7 \textgreater − 3.1 A. X \textgreater 3.9 X \ \textgreater \ 3.9 X \textgreater 3.9 B. X \textgreater − 4.1 X \ \textgreater \ -4.1 X \textgreater − 4.1 C. X \textgreater 4.1 X \ \textgreater \ 4.1 X \textgreater 4.1 D. X \textgreater − 10.1 X \ \textgreater \ -10.1 X \textgreater − 10.1

Introduction

In mathematics, inequalities are used to compare two or more values. 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 linear inequalities, specifically the inequality $x - 7 > -3.1$. We will break down the solution step by step and provide a clear explanation of each step.

What is a Linear Inequality?

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. For example, the inequality $x - 7 > -3.1$ is a linear inequality because it can be written as a linear equation: $x - 7 = -3.1$. However, the inequality symbol $>$ indicates that the solution is not just a single value, but a range of values.

Step 1: Add 7 to Both Sides

To solve the inequality $x - 7 > -3.1$, we need to isolate the variable $x$. We can do this by adding 7 to both sides of the inequality. This will eliminate the negative term and give us a new inequality with only the variable $x$ on one side.

x - 7 > -3.1
x - 7 + 7 > -3.1 + 7
x > 3.9

Step 2: Simplify the Inequality

Now that we have added 7 to both sides, we can simplify the inequality by combining like terms. In this case, there are no like terms to combine, so the inequality remains the same.

x > 3.9

Step 3: Write the Solution in Interval Notation

The solution to the inequality $x > 3.9$ can be written in interval notation as $(3.9, \infty)$. This means that the solution is all values of $x$ that are greater than 3.9.

Conclusion

In conclusion, solving the inequality $x - 7 > -3.1$ involves adding 7 to both sides and simplifying the resulting inequality. The solution is all values of $x$ that are greater than 3.9, which can be written in interval notation as $(3.9, \infty)$.

Answer

The correct answer is:

• A. $x > 3.9$

Why is this the correct answer?

This is the correct answer because we added 7 to both sides of the inequality and simplified the resulting inequality. The solution is all values of $x$ that are greater than 3.9, which is the correct answer.

What are some common mistakes to avoid?

When solving linear inequalities, there are several common mistakes to avoid. These include:

• Adding or subtracting the wrong value to both sides of the inequality
• Not simplifying the inequality after adding or subtracting a value
• Not writing the solution in interval notation

Tips and Tricks

Here are some tips and tricks to help you solve linear inequalities:

• Always add or subtract the same value to both sides of the inequality
• Simplify the inequality after adding or subtracting a value
• Write the solution in interval notation
• Check your work by plugging in a value from the solution set into the original inequality

Real-World Applications

Linear inequalities have many real-world applications. For example, they can be used to model population growth, financial transactions, and physical systems. In addition, linear inequalities can be used to make decisions based on data and to optimize systems.

Conclusion

In conclusion, solving linear inequalities involves adding or subtracting a value to both sides of the inequality and simplifying the resulting inequality. The solution is all values of the variable that satisfy the inequality, which can be written in interval notation. By following the steps outlined in this article, you can solve linear inequalities and apply them to real-world problems.

Final Answer

The final answer is:

• A. $x > 3.9$
  Solving Linear Inequalities: A Q&A Guide =============================================

Introduction

In our previous article, we discussed how to solve linear inequalities, specifically the inequality $x - 7 > -3.1$. We broke down the solution step by step and provided a clear explanation of each step. In this article, we will answer some common questions that students often have when solving linear inequalities.

Q: What is the difference between a linear equation and a linear inequality?

A: A linear equation is an equation that can be written in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants. A linear inequality, on the other hand, is an inequality that can be written in the form of $ax + b > c$, $ax + b < c$, $ax + b \geq c$, or $ax + b \leq c$.

Q: How do I know which direction to add or subtract a value to both sides of the inequality?

A: When solving a linear inequality, you need to add or subtract the same value to both sides of the inequality. If the inequality is of the form $ax + b > c$, you need to add $b$ to both sides of the inequality. If the inequality is of the form $ax + b < c$, you need to subtract $b$ from both sides of the inequality.

Q: What is the difference between a solution set and a solution?

A: A solution set is the set of all values of the variable that satisfy the inequality. A solution, on the other hand, is a single value that satisfies the inequality.

Q: How do I write the solution set in interval notation?

A: To write the solution set in interval notation, you need to use the following notation:

• $(a, b)$: This notation represents all values of the variable that are greater than $a$ and less than $b$.
• $[a, b]$ : This notation represents all values of the variable that are greater than or equal to $a$ and less than or equal to $b$.
• $(a, \infty)$: This notation represents all values of the variable that are greater than $a$.
• $(-\infty, a)$: This notation represents all values of the variable that are less than $a$.

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

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

• Adding or subtracting the wrong value to both sides of the inequality
• Not simplifying the inequality after adding or subtracting a value
• Not writing the solution set in interval notation

Q: How do I check my work when solving a linear inequality?

A: To check your work when solving a linear inequality, you need to plug in a value from the solution set into the original inequality. If the inequality is true, then your solution is correct.

Q: What are some real-world applications of linear inequalities?

A: Linear inequalities have many real-world applications, including:

• Modeling population growth
• Financial transactions
• Physical systems
• Making decisions based on data
• Optimizing systems

Conclusion

In conclusion, solving linear inequalities involves adding or subtracting a value to both sides of the inequality and simplifying the resulting inequality. The solution is all values of the variable that satisfy the inequality, which can be written in interval notation. By following the steps outlined in this article, you can solve linear inequalities and apply them to real-world problems.

Final Answer

The final answer is:

• A. $x > 3.9$