Question
Which statements are true about the solution to the inequality 15≥22+x
? Select the three correct answers.
NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.
(3 points)
Responses
x≥−7
x is greater than or equal to negative 7
x≤−7
x is less than or equal to negative 7
-7 is part of the solution
-7 is part of the solution
The graph has an open circle.
The graph has an open circle.
The graph has a closed circle.
The graph has a closed circle.
-6 is part of the solution
-6 is part of the solution
? Select the three correct answers.
NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.
(3 points)
Responses
x≥−7
x is greater than or equal to negative 7
x≤−7
x is less than or equal to negative 7
-7 is part of the solution
-7 is part of the solution
The graph has an open circle.
The graph has an open circle.
The graph has a closed circle.
The graph has a closed circle.
-6 is part of the solution
-6 is part of the solution
Answers
Answered by
GPT-4o mini
To solve the inequality \( 15 \geq 22 + x \), we first isolate \( x \):
1. Subtract 22 from both sides:
\[
15 - 22 \geq x
\]
This simplifies to:
\[
-7 \geq x
\]
or equivalently:
\[
x \leq -7
\]
Now, we can analyze each statement:
1. **x ≥ −7**: This statement is **false**, because the solution indicates \( x \) must be less than or equal to -7.
2. **x is greater than or equal to negative 7**: This statement is also **false** for the same reason as above.
3. **x ≤ −7**: This statement is **true**, as we calculated that \( x \) can be at most -7.
4. **-7 is part of the solution**: This statement is **true** because -7 is included in the solution set (as the inequality allows for \( x \) to be equal to -7).
5. **The graph has an open circle**: This statement is **false**. The solution includes -7, which means the graph would have a closed circle at -7.
6. **The graph has a closed circle**: This statement is **true** since -7 is included in the solution.
7. **-6 is part of the solution**: This statement is **false** because -6 is greater than -7, and thus not part of the solution.
Based on this analysis, the true statements are:
- \( x \leq -7 \)
- -7 is part of the solution
- The graph has a closed circle.
So the three correct answers are:
1. \( x \leq -7 \)
2. -7 is part of the solution
3. The graph has a closed circle.
1. Subtract 22 from both sides:
\[
15 - 22 \geq x
\]
This simplifies to:
\[
-7 \geq x
\]
or equivalently:
\[
x \leq -7
\]
Now, we can analyze each statement:
1. **x ≥ −7**: This statement is **false**, because the solution indicates \( x \) must be less than or equal to -7.
2. **x is greater than or equal to negative 7**: This statement is also **false** for the same reason as above.
3. **x ≤ −7**: This statement is **true**, as we calculated that \( x \) can be at most -7.
4. **-7 is part of the solution**: This statement is **true** because -7 is included in the solution set (as the inequality allows for \( x \) to be equal to -7).
5. **The graph has an open circle**: This statement is **false**. The solution includes -7, which means the graph would have a closed circle at -7.
6. **The graph has a closed circle**: This statement is **true** since -7 is included in the solution.
7. **-6 is part of the solution**: This statement is **false** because -6 is greater than -7, and thus not part of the solution.
Based on this analysis, the true statements are:
- \( x \leq -7 \)
- -7 is part of the solution
- The graph has a closed circle.
So the three correct answers are:
1. \( x \leq -7 \)
2. -7 is part of the solution
3. The graph has a closed circle.