Number Line Problem: Finding Variable 'a' Between 0 and 5

Q: What does 'a is a positive number less than 5' mean exactly?

This means two things at once: $ a > 0 $ (positive) AND \( a (less than 5). The variable must satisfy both conditions simultaneously.

Q: Why is 0 0, a < 5?

Compound inequality notation \( 0 shows the relationship clearly in one expression. It means 'a is between 0 and 5' which is more precise than separate conditions.

Q: Does the solution include the endpoints 0 and 5?

No! The inequality uses strict inequality symbols (), not ≤ or ≥. So a cannot equal 0 or 5, only values strictly between them like 2.5 or 4.9.

Q: What if I picked answer choice with a = 1?

That's too specific! While a = 1 satisfies the conditions, the variable a can be any value between 0 and 5, like 2.7 or 4.999. Don't limit yourself to just one number.

Interval Notation with Number Line Visualization

$a$ is a positive number less than 5.

Select the correct expression regarding the value of $a$ on the number line:

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Step-by-step written solution

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Understand the problem

$a$ is a positive number less than 5.

Select the correct expression regarding the value of $a$ on the number line:

Step-by-step solution

First, let's mark the expression $a < 5$ on the axis:

Now let's mark the expression $a > 0$ on the axis:

Then we can mark in orange the overlapping segment that represents the expression in question:

$0 < a < 5$

Final Answer

$0 < a < 5$

Key Points to Remember

Essential concepts to master this topic

Compound Inequality: Combine two conditions using logical AND to find overlap
Visualization: Mark $a > 0$ and $a < 5$ separately on number line
Check: Verify solution $0 < a < 5$ includes all valid values ✓

Common Mistakes

Avoid these frequent errors

Writing separate conditions instead of combined inequality
Don't write $a > 0$ , $a < 5$ as two separate statements = incomplete answer! This misses that both conditions must be true simultaneously. Always combine using $0 < a < 5$ to show the intersection.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

What does 'a is a positive number less than 5' mean exactly?

This means two things at once: $a > 0$ (positive) AND $a < 5$ (less than 5). The variable must satisfy both conditions simultaneously.

Why is 0 < a < 5 better than writing a > 0, a < 5?

Compound inequality notation $0 < a < 5$ shows the relationship clearly in one expression. It means 'a is between 0 and 5' which is more precise than separate conditions.

Does the solution include the endpoints 0 and 5?

No! The inequality uses strict inequality symbols (< and >), not ≤ or ≥. So a cannot equal 0 or 5, only values strictly between them like 2.5 or 4.9.

How do I visualize this on a number line?

Draw two separate rays: one starting from 0 going right (for $a > 0$ ) and one ending at 5 going left (for $a < 5$ ). The overlapping region between 0 and 5 is your answer!

What if I picked answer choice with a = 1?

That's too specific! While a = 1 satisfies the conditions, the variable a can be any value between 0 and 5, like 2.7 or 4.999. Don't limit yourself to just one number.

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