Solve the Inequality: Finding the Missing Number in 5,181 < ???9 < 6,001

Q: How do I know which digits to use for the missing places?

Start with the left boundary (5,181) and work systematically. Since the number ends in 9, try 5,189 first. Check if it's greater than 5,181 (yes!) and less than 6,001 (yes!).

Q: Why can't I use 6,009 since it ends in 9?

6,009 is too big! It must be less than 6,001, so any number starting with 6 won't work. The answer must start with 5.

Q: What if there are multiple possible answers?

In this case, there's only one valid answer. The constraints 5,181

Q: How do I write 5,189 in the answer format?

Break it into place values: 5 (thousands), 1 (hundreds), 8 (tens), 9 (ones). So the answer is $ 5,1,8 $.

Q: Can I work backwards from 6,001?

Yes! Start with numbers less than 6,001 that end in 9: try 5,999, 5,989, etc. But remember, it must also be greater than 5,181, so 5,189 is your answer.

Number Comparison with Missing Digits

Complete the following inequality using the given numbers:

$5,181 < ???9 < 6,001$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following inequality using the given numbers:

$5,181 < ???9 < 6,001$

Step-by-step solution

To solve this problem, we need to find a number in the form of $???9$ such that it satisfies $5,181 < ???9 < 6,001$ .

Let's proceed with the following steps:

Step 1: The number must be greater than 5,181. Given the format $???9$ , the smallest number that matches this requirement is 5,189.
Step 2: Verify this number is less than 6,001. The number 5,189 indeed fits this condition as well.
Step 3: Therefore, the correct number is 5,189, conforming to $???9$ format.

Thus, substituting 5,189 into the inequality, we have $5,181 < 5,189 < 6,001$ .

The choice that corresponds to the solution is: $5,1,8$ .

Therefore, the solution to the problem is $5,1,8$ .

Final Answer

$5,1,8$

Key Points to Remember

Essential concepts to master this topic

Format Rule: Missing digits must create valid four-digit number ending in 9
Technique: Start with 5,181 < 5,189: check if 5,189 < 6,001
Check: Verify inequality works: 5,181 < 5,189 < 6,001 ✓

Common Mistakes

Avoid these frequent errors

Ignoring the inequality constraints when filling digits
Don't just focus on the format ???9 without checking both inequality conditions = numbers outside the range! The number must be greater than 5,181 AND less than 6,001. Always verify both parts of the compound inequality.

Practice Quiz

Test your knowledge with interactive questions

Insert the missing digits in order to obtain a number that correctly lies within the given range:

$$ 7,001 < ??98 < 8,100 $$

FAQ

Everything you need to know about this question

How do I know which digits to use for the missing places?

Start with the left boundary (5,181) and work systematically. Since the number ends in 9, try 5,189 first. Check if it's greater than 5,181 (yes!) and less than 6,001 (yes!).

Why can't I use 6,009 since it ends in 9?

6,009 is too big! It must be less than 6,001, so any number starting with 6 won't work. The answer must start with 5.

What if there are multiple possible answers?

In this case, there's only one valid answer. The constraints 5,181 < ???9 < 6,001 with the format ???9 give us exactly one possibility: 5,189.

How do I write 5,189 in the answer format?

Break it into place values: 5 (thousands), 1 (hundreds), 8 (tens), 9 (ones). So the answer is $5,1,8$ .

Can I work backwards from 6,001?

Yes! Start with numbers less than 6,001 that end in 9: try 5,999, 5,989, etc. But remember, it must also be greater than 5,181, so 5,189 is your answer.

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