Solving 5 < -5: Understanding Number Line Inequalities

Q: Why isn't 5 < -5 true if both numbers have the same absolute value?

Great question! Even though $ |5| = |-5| = 5 $, the negative sign makes -5 smaller. On a number line, -5 is to the left of 5, which means -5

Q: How do I remember which direction the inequality goes?

Think of the number line! Numbers get larger as you move right and smaller as you move left. Since 5 is to the right of -5, we have 5 > -5.

Q: Are there any cases where a negative number is greater than a positive number?

Never! Any positive number is always greater than any negative number. This is a fundamental rule: positive > 0 > negative.

Q: What if I see something like -2 compared to -8?

Both are negative, so use the number line! -2 is to the right of -8, making -2 > -8. The number closer to zero is always larger when both are negative.

Q: Does the size of the numbers matter when comparing positive and negative?

No! Even tiny positive numbers like $ 0.001 $ are greater than huge negative numbers like -1000. The sign determines the comparison: $ 0.001 > -1000 $.

Number Line Comparisons with Positive and Negative Numbers

$5 < -5$

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Understand the problem

$5 < -5$

Step-by-step solution

As per the fact that there cannot be a situation where a negative number is greater than a positive number, the answer is incorrect.

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Rule: Positive numbers are always greater than negative numbers
Technique: Use number line position: 5 is right of -5, so 5 > -5
Check: Compare positions: -5 is left of 5 on the number line ✓

Common Mistakes

Avoid these frequent errors

Confusing absolute value with actual value
Don't think that -5 > 5 because |-5| = 5! The negative sign makes -5 smaller than any positive number. Always remember that negative numbers are less than positive numbers, regardless of their absolute values.

Practice Quiz

Test your knowledge with interactive questions

All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

Why isn't 5 < -5 true if both numbers have the same absolute value?

Great question! Even though $|5| = |-5| = 5$ , the negative sign makes -5 smaller. On a number line, -5 is to the left of 5, which means -5 < 5, not 5 < -5.

How do I remember which direction the inequality goes?

Think of the number line! Numbers get larger as you move right and smaller as you move left. Since 5 is to the right of -5, we have 5 > -5.

Are there any cases where a negative number is greater than a positive number?

Never! Any positive number is always greater than any negative number. This is a fundamental rule: positive > 0 > negative.

What if I see something like -2 compared to -8?

Both are negative, so use the number line! -2 is to the right of -8, making -2 > -8. The number closer to zero is always larger when both are negative.

Does the size of the numbers matter when comparing positive and negative?

No! Even tiny positive numbers like $0.001$ are greater than huge negative numbers like -1000. The sign determines the comparison: $0.001 > -1000$ .

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