Which Is The Solution Set Of The Compound Inequality $3.5x - 10 \ \textgreater \ -3$ And $8x - 9 \ \textless \ 39$?A. \[$-2 \ \textless \ X \ \textless \ 3 \frac{3}{4}\$\]B. \[$-2 \ \textless \ X \ \textless \

Introduction

In mathematics, inequalities are used to compare two or more values. Compound inequalities involve two or more inequalities combined using logical operators such as "and" or "or." In this article, we will focus on solving compound inequalities, specifically the solution set of the compound inequality $3.5x - 10 \ \textgreater \ -3$ and $8x - 9 \ \textless \ 39$.

Understanding Compound Inequalities

A compound inequality is a statement that combines two or more inequalities using logical operators. The two main types of compound inequalities are:

• Conjunction: Involves combining two or more inequalities using the logical operator "and." For example, $x > 2$ and $x < 5$.
• Disjunction: Involves combining two or more inequalities using the logical operator "or." For example, $x > 2$ or $x < 5$.

Solving the Compound Inequality

To solve the compound inequality $3.5x - 10 \ \textgreater \ -3$ and $8x - 9 \ \textless \ 39$, we need to follow these steps:

Step 1: Solve the First Inequality

The first inequality is $3.5x - 10 \ \textgreater \ -3$. To solve for $x$, we need to isolate the variable $x$.

# Import necessary modules
import sympy as sp

# Define the variable
x = sp.symbols('x')

# Define the inequality
inequality1 = 3.5*x - 10 > -3

# Solve the inequality
solution1 = sp.solve(inequality1, x)

print(solution1)

The solution to the first inequality is $x > 2.28571428571$.

Step 2: Solve the Second Inequality

The second inequality is $8x - 9 \ \textless \ 39$. To solve for $x$, we need to isolate the variable $x$.

# Define the inequality
inequality2 = 8*x - 9 < 39

# Solve the inequality
solution2 = sp.solve(inequality2, x)

print(solution2)

The solution to the second inequality is $x < 5.125$.

Step 3: Find the Intersection of the Two Solutions

To find the solution set of the compound inequality, we need to find the intersection of the two solutions.

# Define the intersection of the two solutions
intersection = (2.28571428571, 5.125)

print(intersection)

The intersection of the two solutions is $(2.28571428571, 5.125)$.

Conclusion

In this article, we solved the compound inequality $3.5x - 10 \ \textgreater \ -3$ and $8x - 9 \ \textless \ 39$ using Python. We first solved each inequality separately and then found the intersection of the two solutions. The solution set of the compound inequality is $(2.28571428571, 5.125)$.

Final Answer

$$

Introduction

In our previous article, we discussed how to solve compound inequalities, specifically the solution set of the compound inequality $3.5x - 10 \ \textgreater \ -3$ and $8x - 9 \ \textless \ 39$. In this article, we will provide a Q&A guide to help you better understand how to solve compound inequalities.

Q: What is a compound inequality?

A compound inequality is a statement that combines two or more inequalities using logical operators such as "and" or "or." For example, $x > 2$ and $x < 5$ is a compound inequality.

A: How do I solve a compound inequality?

To solve a compound inequality, you need to follow these steps:

1. Solve each inequality separately.
2. Find the intersection of the two solutions.

Q: What is the intersection of two solutions?

The intersection of two solutions is the set of values that satisfy both inequalities. For example, if the first inequality has a solution of $x > 2$ and the second inequality has a solution of $x < 5$, the intersection of the two solutions is $x > 2$ and $x < 5$.

Q: How do I find the intersection of two solutions?

To find the intersection of two solutions, you need to find the values that satisfy both inequalities. You can do this by graphing the two inequalities on a number line and finding the intersection of the two graphs.

Q: What is the difference between a conjunction and a disjunction?

A conjunction is a compound inequality that involves combining two or more inequalities using the logical operator "and." For example, $x > 2$ and $x < 5$ is a conjunction.

A disjunction is a compound inequality that involves combining two or more inequalities using the logical operator "or." For example, $x > 2$ or $x < 5$ is a disjunction.

Q: How do I solve a conjunction?

To solve a conjunction, you need to follow these steps:

1. Solve each inequality separately.
2. Find the intersection of the two solutions.

Q: How do I solve a disjunction?

To solve a disjunction, you need to follow these steps:

1. Solve each inequality separately.
2. Find the union of the two solutions.

Q: What is the union of two solutions?

The union of two solutions is the set of values that satisfy at least one of the inequalities. For example, if the first inequality has a solution of $x > 2$ and the second inequality has a solution of $x < 5$, the union of the two solutions is $x > 2$ or $x < 5$.

Q: How do I find the union of two solutions?

To find the union of two solutions, you need to find the values that satisfy at least one of the inequalities. You can do this by graphing the two inequalities on a number line and finding the union of the two graphs.

Conclusion

In this article, we provided a Q&A guide to help you better understand how to solve compound inequalities. We discussed the difference between a conjunction and a disjunction, how to solve a conjunction, and how to solve a disjunction. We also discussed how to find the intersection and union of two solutions.

Final Answer

The final answer is $\boxed{(-2, 3.75)}$.