Question
Solve and graph the solution to the inequality −6n+3≥21
on your own paper or device. In the box below, give the solution to the inequality and describe how your graph looks.(2 points)
Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
on your own paper or device. In the box below, give the solution to the inequality and describe how your graph looks.(2 points)
Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
Answers
GPT-4o mini
Let's solve the inequality step by step.
Given the inequality:
\[
-6n + 3 \geq 21
\]
### Step 1: Isolate the term with \(n\)
First, we will subtract 3 from both sides:
\[
-6n + 3 - 3 \geq 21 - 3
\]
This simplifies to:
\[
-6n \geq 18
\]
### Step 2: Solve for \(n\)
Next, we divide both sides by -6. Remember, when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign:
\[
n \leq \frac{18}{-6}
\]
This simplifies to:
\[
n \leq -3
\]
### Conclusion
The solution to the inequality is:
\[
n \leq -3
\]
### Graph Description
To graph this inequality on a number line:
1. Draw a horizontal line representing the number line.
2. Place a closed circle or dot at -3 to indicate that -3 is included in the solution (because it has the "less than or equal to" sign).
3. Shade to the left of -3 to represent all numbers less than -3.
Overall, the graph will show a solid dot at -3 with a shaded line extending to the left, indicating all numbers less than or equal to -3 are part of the solution.
Given the inequality:
\[
-6n + 3 \geq 21
\]
### Step 1: Isolate the term with \(n\)
First, we will subtract 3 from both sides:
\[
-6n + 3 - 3 \geq 21 - 3
\]
This simplifies to:
\[
-6n \geq 18
\]
### Step 2: Solve for \(n\)
Next, we divide both sides by -6. Remember, when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign:
\[
n \leq \frac{18}{-6}
\]
This simplifies to:
\[
n \leq -3
\]
### Conclusion
The solution to the inequality is:
\[
n \leq -3
\]
### Graph Description
To graph this inequality on a number line:
1. Draw a horizontal line representing the number line.
2. Place a closed circle or dot at -3 to indicate that -3 is included in the solution (because it has the "less than or equal to" sign).
3. Shade to the left of -3 to represent all numbers less than -3.
Overall, the graph will show a solid dot at -3 with a shaded line extending to the left, indicating all numbers less than or equal to -3 are part of the solution.