Solve the Inequality: Proving -2 < 0 on a Number Line

Q: Why is -2 less than 0 if 2 is bigger than 0?

The negative sign flips everything! Think of it like temperature: -2°F is colder (smaller) than 0°F, even though 2°F would be warmer than 0°F.

Q: How do I remember which way inequalities go with negative numbers?

Use the number line! Numbers get smaller as you move left and bigger as you move right. Since -2 is to the left of 0, we know \( -2 .

Q: Are all negative numbers less than zero?

Yes, always! Every negative number is less than zero. This includes fractions like $ -\frac{1}{2} $, decimals like -0.1, and large numbers like -100.

Q: What if I see -2 < 0 on a test - is this always true?

This statement is always true! It's a mathematical fact. Any inequality showing a negative number less than zero will always be correct.

Q: How does this help with harder inequality problems?

Understanding that negatives are always less than zero helps you check your work in complex problems. If your final answer says a negative equals a positive, you know something went wrong!

Number Line Inequalities with Negative Values

$-2 < 0$

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Understand the problem

$-2 < 0$

Step-by-step solution

Since every negative number is necessarily less than zero, the answer is indeed correct

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Rule: All negative numbers are always less than zero
Technique: Use number line position: -2 is left of 0
Check: Verify on number line: -2 position confirms it's less than 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing negative with positive comparisons
Don't think -2 is greater than 0 because 2 > 0 = completely wrong direction! Negative signs change the comparison completely. Always remember negative numbers are smaller than zero and get smaller as they move left on the number line.

Practice Quiz

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What is the distance between 0 and F?

FAQ

Everything you need to know about this question

Why is -2 less than 0 if 2 is bigger than 0?

The negative sign flips everything! Think of it like temperature: -2°F is colder (smaller) than 0°F, even though 2°F would be warmer than 0°F.

How do I remember which way inequalities go with negative numbers?

Use the number line! Numbers get smaller as you move left and bigger as you move right. Since -2 is to the left of 0, we know $-2 < 0$ .

Are all negative numbers less than zero?

Yes, always! Every negative number is less than zero. This includes fractions like $-\frac{1}{2}$ , decimals like -0.1, and large numbers like -100.

What if I see -2 < 0 on a test - is this always true?

This statement is always true! It's a mathematical fact. Any inequality showing a negative number less than zero will always be correct.

How does this help with harder inequality problems?

Understanding that negatives are always less than zero helps you check your work in complex problems. If your final answer says a negative equals a positive, you know something went wrong!

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