Identify the Missing Number in the Range Between 51,170 and 51,190

Q: What does the box symbol mean in this inequality?

The box □ represents the missing number you need to find. It's like a placeholder that should be replaced with a value that makes the inequality true.

Q: Can the answer be exactly 51,170 or 51,190?

No! The symbols mean strictly less than and strictly greater than. The answer must be between these values, but cannot equal them.

Q: How do I quickly check if a number fits in the range?

Use a two-step check:Is the number greater than 51,170? ✓Is the number less than 51,190? ✓If both are true, it's correct!

Q: What if multiple answers seem to fit?

Double-check your comparisons! Only one number should satisfy both conditions. If you think multiple answers work, recheck each number carefully against both inequality signs.

Q: Why is 51,085 wrong when it's close to the range?

\( 51,085 , so it's too small to be in our range. Remember, we need a number greater than 51,170, not less than it.

Inequality Solutions with Integer Bounds

Fill in the missing number:

$51,170 < \Box < 51,190$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing number:

$51,170 < \Box < 51,190$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the range defined by the inequality $51,170 < \Box < 51,190$ .
Step 2: Compare each answer choice against this range.

Now, let's work through each step:

Step 1: The problem specifies a range from 51,170 to 51,190. We need a value that is greater than 51,170 but less than 51,190.

Step 2: Checking each choice:
- Choice 1: $51,085$ is less than 51,170, so it does not satisfy the condition.
- Choice 2: $51,182$ is greater than 51,170 and less than 51,190. This satisfies the condition.
- Choice 3: $51,192$ is greater than 51,190, so it does not satisfy the condition.
- Choice 4: $51,162$ is less than 51,170, so it does not satisfy the condition.

Therefore, the solution to the problem is $51,182$ .

Final Answer

$51,182$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Number must be between lower and upper bounds
Technique: Check each option: 51,182 > 51,170 and < 51,190
Check: Verify bounds: 51,170 < 51,182 < 51,190 is true ✓

Common Mistakes

Avoid these frequent errors

Confusing inequality symbols with equality
Don't treat < and > like = signs when checking answers = wrong boundary inclusion! Students often think 51,170 or 51,190 could be correct answers. Always remember that < means 'less than' and excludes the boundary value itself.

Practice Quiz

Test your knowledge with interactive questions

Select the appropriate sign:

$24,909\Box24,990$

FAQ

Everything you need to know about this question

What does the box symbol mean in this inequality?

The box □ represents the missing number you need to find. It's like a placeholder that should be replaced with a value that makes the inequality true.

Can the answer be exactly 51,170 or 51,190?

No! The symbols < and > mean strictly less than and strictly greater than. The answer must be between these values, but cannot equal them.

How do I quickly check if a number fits in the range?

Use a two-step check:

Is the number greater than 51,170? ✓
Is the number less than 51,190? ✓

If both are true, it's correct!

What if multiple answers seem to fit?

Double-check your comparisons! Only one number should satisfy both conditions. If you think multiple answers work, recheck each number carefully against both inequality signs.

Why is 51,085 wrong when it's close to the range?

$51,085 < 51,170$ , so it's too small to be in our range. Remember, we need a number greater than 51,170, not less than it.

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