Find Variable 'a': Expressing Numbers Between 3 and 7 on Number Line

Q: What does 3 < a < 7 actually mean in words?

It means 'a is greater than 3 AND less than 7'. The variable a must satisfy both conditions at the same time. So a could be 4, 5, 6, or any decimal between 3 and 7.

Q: Why can't a equal 3 or 7?

Because we use the , not ≤. The not included. If 3 and 7 were included, we'd write 3 ≤ a ≤ 7.

Q: How do I know which answer choice is correct?

Look for the expression that shows both conditions: a > 3 AND a \( 3 . Avoid single equalities like a = 7 or impossible ranges like 7

Q: What would the number line look like for this inequality?

Draw open circles at 3 and 7 (since they're not included), then shade the region between them. This shows all possible values of a that make both 3

Compound Inequalities with Number Line Representation

Select a compatible expression to show that a is greater than 3 but smaller than 7:

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Understand the problem

Select a compatible expression to show that a is greater than 3 but smaller than 7:

Step-by-step solution

First, we'll mark on the axis the expression $a > 3$

Then we'll mark on the axis the expression $a < 7$

We'll mark in orange the segment representing the requested expression:

$3 < a < 7$

Final Answer

$3 < a < 7$

Key Points to Remember

Essential concepts to master this topic

Compound Inequalities: Two conditions connected by 'and' must both be true
Technique: 3 < a < 7 means a > 3 AND a < 7
Check: Test values like a = 5: 3 < 5 < 7 is true ✓

Common Mistakes

Avoid these frequent errors

Reading inequality symbols incorrectly
Don't confuse 3 < a < 7 with 7 < a < 3 = impossible range! The first number must be smaller than the second for a valid interval. Always read left to right: 'a is greater than 3 AND less than 7'.

Practice Quiz

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What is the distance between 0 and F?

FAQ

Everything you need to know about this question

What does 3 < a < 7 actually mean in words?

It means 'a is greater than 3 AND less than 7'. The variable a must satisfy both conditions at the same time. So a could be 4, 5, 6, or any decimal between 3 and 7.

Why can't a equal 3 or 7?

Because we use the < symbol, not ≤. The < symbol means 'strictly less than' or 'strictly greater than', so the endpoints are not included. If 3 and 7 were included, we'd write 3 ≤ a ≤ 7.

How do I know which answer choice is correct?

Look for the expression that shows both conditions: a > 3 AND a < 7. This is written as $3 < a < 7$ . Avoid single equalities like a = 7 or impossible ranges like 7 < a < 3.

What would the number line look like for this inequality?

Draw open circles at 3 and 7 (since they're not included), then shade the region between them. This shows all possible values of a that make both 3 < a and a < 7 true.

Can I give a specific example of a value that works?

Yes! Try a = 5: Is 3 < 5? Yes. Is 5 < 7? Yes. Since both conditions are true, a = 5 is in our solution set. Values like 2.5 or 8 would fail one of the conditions.

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