Question
solve and graph the solution to the inequality (-6n+3 greater than or equal to 21). then explain what the solution means.
(write like a 7th grader)
(write like a 7th grader)
Answers
GPT-4o mini
To solve the inequality \(-6n + 3 \geq 21\), we need to get \(n\) by itself. Here’s how to do it step by step:
1. **Subtract 3 from both sides:**
\(-6n + 3 - 3 \geq 21 - 3\)
This simplifies to:
\(-6n \geq 18\)
2. **Now, divide both sides by -6:**
\(-6n / -6 \leq 18 / -6\)
Remember, when you divide by a negative number, you have to flip the inequality sign!
So we get:
\(n \leq -3\)
Now that we have solved the inequality, \(n \leq -3\) means that \(n\) can be any number that is less than or equal to \(-3\).
### Graphing the Solution:
To graph this on a number line:
1. Draw a horizontal line and mark some numbers. Make sure to include \(-4, -3, -2, -1, 0\) and so on.
2. For \(-3\), put a closed dot (●) on the number line because \(-3\) is included in the solution (the inequality is "less than or equal to").
3. Shade the line to the left of \(-3\) because it includes all numbers less than \(-3\).
### Explanation of the Solution:
The solution \(n \leq -3\) means that any number that is \(-3\) or smaller is valid. For example, \(-4\), \(-5\), or even \(-10\) are all solutions. If you were using this in a real-life situation, it could mean something like having a certain amount of money that is less than or equal to \(-$3.00$, which might mean you owe money or are in debt. So it helps understand what values of \(n\) are acceptable based on the inequality!
1. **Subtract 3 from both sides:**
\(-6n + 3 - 3 \geq 21 - 3\)
This simplifies to:
\(-6n \geq 18\)
2. **Now, divide both sides by -6:**
\(-6n / -6 \leq 18 / -6\)
Remember, when you divide by a negative number, you have to flip the inequality sign!
So we get:
\(n \leq -3\)
Now that we have solved the inequality, \(n \leq -3\) means that \(n\) can be any number that is less than or equal to \(-3\).
### Graphing the Solution:
To graph this on a number line:
1. Draw a horizontal line and mark some numbers. Make sure to include \(-4, -3, -2, -1, 0\) and so on.
2. For \(-3\), put a closed dot (●) on the number line because \(-3\) is included in the solution (the inequality is "less than or equal to").
3. Shade the line to the left of \(-3\) because it includes all numbers less than \(-3\).
### Explanation of the Solution:
The solution \(n \leq -3\) means that any number that is \(-3\) or smaller is valid. For example, \(-4\), \(-5\), or even \(-10\) are all solutions. If you were using this in a real-life situation, it could mean something like having a certain amount of money that is less than or equal to \(-$3.00$, which might mean you owe money or are in debt. So it helps understand what values of \(n\) are acceptable based on the inequality!