Which Compound Inequality Can Be Used To Solve The Inequality $|3x + 2| \ \textgreater \ 7$?A. $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$B. $-7 \ \textgreater \ 3x + 2 \ \textgreater \ 7$C. $3x + 2 \

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Introduction

When dealing with absolute value inequalities, it's essential to understand how to rewrite them as compound inequalities. This process involves creating two separate inequalities that represent the two possible cases for the absolute value expression. In this article, we will explore how to solve the inequality $|3x + 2| \ \textgreater \ 7$ and determine which compound inequality can be used to solve it.

Understanding Absolute Value Inequalities

Absolute value inequalities involve the absolute value of an expression being greater than, less than, or equal to a certain value. The absolute value of an expression is its distance from zero on the number line, without considering direction. When dealing with absolute value inequalities, we need to consider two cases: one where the expression inside the absolute value is positive, and another where it is negative.

Solving the Inequality $|3x + 2| \ \textgreater \ 7$

To solve the inequality $|3x + 2| \ \textgreater \ 7$, we need to consider the two possible cases:

• Case 1: $3x + 2 \ \textgreater \ 7$
• Case 2: $3x + 2 \ \textless \ -7$

Case 1: $3x + 2 \ \textgreater \ 7$

To solve the inequality $3x + 2 \ \textgreater \ 7$, we need to isolate the variable $x$. We can do this by subtracting 2 from both sides of the inequality and then dividing both sides by 3.

# Case 1: 3x + 2 > 7
# Subtract 2 from both sides
# 3x > 5
# Divide both sides by 3
x > 5/3

Case 2: $3x + 2 \ \textless \ -7$

To solve the inequality $3x + 2 \ \textless \ -7$, we need to isolate the variable $x$. We can do this by subtracting 2 from both sides of the inequality and then dividing both sides by 3.

# Case 2: 3x + 2 < -7
# Subtract 2 from both sides
# 3x < -9
# Divide both sides by 3
x < -3

Combining the Two Cases

Now that we have solved the two cases, we can combine them to get the final solution. The solution to the inequality $|3x + 2| \ \textgreater \ 7$ is:

# Solution: x > 5/3 or x < -3

Which Compound Inequality Can Be Used to Solve the Inequality?

Now that we have solved the inequality $|3x + 2| \ \textgreater \ 7$, we can determine which compound inequality can be used to solve it. The compound inequality that can be used to solve the inequality is:

# Compound Inequality: -7 < 3x + 2 < 7

This compound inequality represents the two possible cases for the absolute value expression: $3x + 2 \ \textgreater \ 7$ and $3x + 2 \ \textless \ -7$.

Conclusion

In this article, we have explored how to solve the inequality $|3x + 2| \ \textgreater \ 7$ and determine which compound inequality can be used to solve it. We have seen that the compound inequality $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$ can be used to solve the inequality. This compound inequality represents the two possible cases for the absolute value expression and can be used to find the solution to the inequality.

Frequently Asked Questions

• Q: What is the solution to the inequality $|3x + 2| \ \textgreater \ 7$? A: The solution to the inequality $|3x + 2| \ \textgreater \ 7$ is $x \ \textgreater \ 5/3$ or $x \ \textless \ -3$.
• Q: Which compound inequality can be used to solve the inequality $|3x + 2| \ \textgreater \ 7$? A: The compound inequality $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$ can be used to solve the inequality.

References

• Absolute Value Inequalities
• Compound Inequalities

Further Reading

• Solving Absolute Value Inequalities
• Compound Inequalities
  

Introduction

In our previous article, we explored how to solve the inequality $|3x + 2| \ \textgreater \ 7$ and determine which compound inequality can be used to solve it. In this article, we will answer some frequently asked questions about absolute value inequalities and compound inequalities.

Q&A

Q: What is the difference between an absolute value inequality and a compound inequality?

A: An absolute value inequality involves the absolute value of an expression being greater than, less than, or equal to a certain value. A compound inequality, on the other hand, involves two separate inequalities that are combined using the word "and" or "or".

Q: How do I solve an absolute value inequality?

A: To solve an absolute value inequality, you need to consider two cases: one where the expression inside the absolute value is positive, and another where it is negative. You can then solve each case separately and combine the solutions to get the final answer.

Q: What is the solution to the inequality $|3x + 2| \ \textgreater \ 7$?

A: The solution to the inequality $|3x + 2| \ \textgreater \ 7$ is $x \ \textgreater \ 5/3$ or $x \ \textless \ -3$.

Q: Which compound inequality can be used to solve the inequality $|3x + 2| \ \textgreater \ 7$?

A: The compound inequality $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$ can be used to solve the inequality.

Q: How do I determine which compound inequality to use?

A: To determine which compound inequality to use, you need to consider the two possible cases for the absolute value expression. You can then combine the two cases to get the final compound inequality.

Q: What is the difference between a "greater than" and a "less than" compound inequality?

A: A "greater than" compound inequality involves two inequalities that are combined using the word "and" and the greater than symbol. A "less than" compound inequality, on the other hand, involves two inequalities that are combined using the word "and" and the less than symbol.

Q: How do I solve a compound inequality?

A: To solve a compound inequality, you need to solve each inequality separately and then combine the solutions to get the final answer.

Q: What is the solution to the compound inequality $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$?

A: The solution to the compound inequality $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$ is $x \ \textgreater \ 5/3$ or $x \ \textless \ -3$.

Conclusion

In this article, we have answered some frequently asked questions about absolute value inequalities and compound inequalities. We have seen that absolute value inequalities involve the absolute value of an expression being greater than, less than, or equal to a certain value, while compound inequalities involve two separate inequalities that are combined using the word "and" or "or". We have also seen how to solve absolute value inequalities and compound inequalities, and how to determine which compound inequality to use.

Frequently Asked Questions

• Q: What is the difference between an absolute value inequality and a compound inequality? A: An absolute value inequality involves the absolute value of an expression being greater than, less than, or equal to a certain value. A compound inequality, on the other hand, involves two separate inequalities that are combined using the word "and" or "or".
• Q: How do I solve an absolute value inequality? A: To solve an absolute value inequality, you need to consider two cases: one where the expression inside the absolute value is positive, and another where it is negative. You can then solve each case separately and combine the solutions to get the final answer.
• Q: What is the solution to the inequality $|3x + 2| \ \textgreater \ 7$? A: The solution to the inequality $|3x + 2| \ \textgreater \ 7$ is $x \ \textgreater \ 5/3$ or $x \ \textless \ -3$.
• Q: Which compound inequality can be used to solve the inequality $|3x + 2| \ \textgreater \ 7$? A: The compound inequality $-7 \ \textless \ 3x + 2 \ \textgreater \ 7$ can be used to solve the inequality.

References

• Absolute Value Inequalities
• Compound Inequalities

Further Reading

• Solving Absolute Value Inequalities
• Compound Inequalities