Which Of The Following Values Are Solutions To The Inequality $x - 7 \ \textless \ 5$?I. 12 II. 5 III. 16 A. None B. I Only C. II Only D. III Only E. I And II F. I And III G. II And III H. I, II, And III

Understanding the Inequality

The given inequality is $x - 7 < 5$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. We can do this by adding 7 to both sides of the inequality.

Step 1: Add 7 to Both Sides

When we add 7 to both sides of the inequality, we get:

$x - 7 + 7 < 5 + 7$

This simplifies to:

$x < 12$

Step 2: Analyze the Solutions

Now that we have the solution to the inequality, we can analyze which of the given values satisfy this solution.

I. 12

The value 12 does not satisfy the inequality $x < 12$, because it is equal to 12, not less than 12.

II. 5

The value 5 satisfies the inequality $x < 12$, because it is less than 12.

III. 16

The value 16 does not satisfy the inequality $x < 12$, because it is greater than 12.

Conclusion

Based on the analysis, the only value that satisfies the inequality $x - 7 < 5$ is II. 5.

The final answer is C. II only.

Understanding the Inequality

The given inequality is $x - 7 < 5$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. We can do this by adding 7 to both sides of the inequality.

Q&A Guide

Q: What is the first step in solving the inequality?

A: The first step in solving the inequality is to add 7 to both sides of the inequality.

Q: What is the resulting inequality after adding 7 to both sides?

A: The resulting inequality after adding 7 to both sides is $x < 12$.

Q: How do we determine which values satisfy the inequality?

A: To determine which values satisfy the inequality, we need to compare each value to the solution of the inequality, which is $x < 12$.

Q: What is the value of x in the inequality $x - 7 < 5$?

A: The value of x in the inequality $x - 7 < 5$ is $x < 12$.

Q: Which of the following values satisfy the inequality $x < 12$?

A: The values that satisfy the inequality $x < 12$ are all values less than 12.

Q: Which of the following values do not satisfy the inequality $x < 12$?

A: The values that do not satisfy the inequality $x < 12$ are all values greater than or equal to 12.

Q: What is the solution to the inequality $x - 7 < 5$?

A: The solution to the inequality $x - 7 < 5$ is $x < 12$.

Q: Which of the following values satisfy the inequality $x < 12$?

A: The values that satisfy the inequality $x < 12$ are all values less than 12.

Q: Which of the following values do not satisfy the inequality $x < 12$?

A: The values that do not satisfy the inequality $x < 12$ are all values greater than or equal to 12.

Conclusion

Based on the Q&A guide, we can conclude that the solution to the inequality $x - 7 < 5$ is $x < 12$. The values that satisfy this inequality are all values less than 12.

Frequently Asked Questions

Q: What is the first step in solving the inequality?

A: The first step in solving the inequality is to add 7 to both sides of the inequality.

Q: What is the resulting inequality after adding 7 to both sides?

A: The resulting inequality after adding 7 to both sides is $x < 12$.

Q: How do we determine which values satisfy the inequality?

A: To determine which values satisfy the inequality, we need to compare each value to the solution of the inequality, which is $x < 12$.

Common Mistakes

Mistake 1: Not adding 7 to both sides of the inequality

A: When solving the inequality, it is essential to add 7 to both sides of the inequality to isolate the variable x.

Mistake 2: Not comparing values to the solution of the inequality

A: When determining which values satisfy the inequality, it is essential to compare each value to the solution of the inequality, which is $x < 12$.

Conclusion

In conclusion, solving the inequality $x - 7 < 5$ requires adding 7 to both sides of the inequality and comparing values to the solution of the inequality, which is $x < 12$. By following these steps, we can determine which values satisfy the inequality.

Final Answer

The final answer is C. II only.