Question
Which values make the inequality true? Choose all that apply. \( 10 \geq 2 n \)
Ask by Fernandez Dawson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
All values of \( n \) that are less than or equal to 5 make the inequality \( 10 \geq 2n \) true.
Solution
Solve the equation by following steps:
- step0: Solve for \(n\):
\(10=2n\)
- step1: Swap the sides:
\(2n=10\)
- step2: Divide both sides:
\(\frac{2n}{2}=\frac{10}{2}\)
- step3: Divide the numbers:
\(n=5\)
To solve the inequality \( 10 \geq 2n \), we first find the equality case by solving the equation \( 10 = 2n \).
1. **Solve for \( n \)**:
\[
10 = 2n
\]
Dividing both sides by 2 gives:
\[
n = 5
\]
2. **Determine the inequality**:
The inequality \( 10 \geq 2n \) can be rewritten as:
\[
n \leq 5
\]
Thus, the values that make the inequality true are all values of \( n \) that are less than or equal to 5. This includes:
- \( n = 5 \)
- Any value less than 5 (e.g., 4, 3, 2, 1, 0, -1, etc.)
In conclusion, the values that satisfy the inequality \( 10 \geq 2n \) are all \( n \) such that \( n \leq 5 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the inequality \( 10 \geq 2n \), we can divide both sides by 2, giving us \( 5 \geq n \) or \( n \leq 5 \). This means that any value of \( n \) that is less than or equal to 5 will satisfy the inequality. So, values like 5, 4, 3, 2, 1, 0, and even negative values will work! Understanding inequalities can be super useful in real life! For example, if you're planning a party and you want to keep the guest list to 5 people or less, knowing how to handle inequalities can help you make sure you don’t go over that number. Just think of it as balancing your guest count while keeping the fun factor high!
