Fill in the Missing Number: Solve the Inequality from 82,695 to 83,100

Q: What does the symbol < mean in this context?

The symbol "strictly less than". So \( 82,695 means the missing number must be greater than 82,695 AND less than 83,100.

Q: Can the missing number equal 82,695 or 83,100?

No! The between 82,695 and 83,100, but not equal to either endpoint.

Q: How do I find a valid number for this inequality?

Pick any number between the two bounds! For example, 82,800 or 82,900 would work perfectly since both are greater than 82,695 and less than 83,100.

Q: Why is 82,200 wrong if it's close to the range?

Even though 82,200 is close, it's less than 82,695, which violates the first condition. In compound inequalities, both parts must be satisfied - there's no "close enough"!

Q: What if none of the given options work?

That's exactly what happened here! When all provided options fail to satisfy the inequality, the correct answer is "None of the answers are correct." Always verify each option systematically.

Q: How can I double-check my work with inequalities?

For each potential answer, ask: Is it greater than the left number? and Is it less than the right number? Only if both answers are "yes" is the option correct.

Compound Inequalities with Range Analysis

Fill in the missing number:

$82,695 < \Box < 83,100$

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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:

$82,695 < \Box < 83,100$

Step-by-step solution

After analyzing each of the given choices:

Option 1: $82,200$ is less than $82,695$ and thus does not satisfy the condition.
Option 2: $83,200$ is greater than $83,100$ and thus does not satisfy the condition.
Option 3: $82,450$ is less than $82,695$ and thus does not satisfy the condition.
Option 4: None of the answers are correct, which matches our analysis.

Therefore, the correct answer is None of the answers are correct.

Final Answer

None of the answers are correct

Key Points to Remember

Essential concepts to master this topic

Range Rule: Number must be greater than left bound AND less than right bound
Technique: Check each option: 82,200 < 82,695 fails the first condition
Verification: Valid numbers must satisfy both 82,695 < x < 83,100 conditions ✓

Common Mistakes

Avoid these frequent errors

Only checking one side of the inequality
Don't just verify x > 82,695 and ignore x < 83,100 = accepting invalid answers! Both conditions must be true simultaneously. Always check that your number falls between BOTH bounds of the compound inequality.

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 symbol < mean in this context?

The symbol < means "strictly less than". So $82,695 < \Box < 83,100$ means the missing number must be greater than 82,695 AND less than 83,100.

Can the missing number equal 82,695 or 83,100?

No! The < symbol means strictly less than, so the number cannot equal the bounds. It must be somewhere between 82,695 and 83,100, but not equal to either endpoint.

How do I find a valid number for this inequality?

Pick any number between the two bounds! For example, 82,800 or 82,900 would work perfectly since both are greater than 82,695 and less than 83,100.

Why is 82,200 wrong if it's close to the range?

Even though 82,200 is close, it's less than 82,695, which violates the first condition. In compound inequalities, both parts must be satisfied - there's no "close enough"!

What if none of the given options work?

That's exactly what happened here! When all provided options fail to satisfy the inequality, the correct answer is "None of the answers are correct." Always verify each option systematically.

How can I double-check my work with inequalities?

For each potential answer, ask: Is it greater than the left number? and Is it less than the right number? Only if both answers are "yes" is the option correct.

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