Number Line Inequality: Proving B > A Using Position Analysis

Q: Why is -4 greater than -5 if 5 is bigger than 4?

Think of negative numbers as debt! Having $4 in debt is better than having $5 in debt. On a number line, moving right always means getting bigger, regardless of positive or negative.

Q: How do I remember the order of negative numbers?

Use the temperature trick: -4°F is warmer (greater) than -5°F. The closer a negative number is to zero, the larger it is!

Q: What if the letters were in different positions?

Always locate each letter's numerical value first, then compare those numbers. The physical position on the number line tells you everything you need to know.

Q: Can I just look at the number line without finding exact values?

Yes! Since B is to the right of A on the number line, B must be greater than A. Moving right always means increasing value.

Q: What if both numbers were positive?

The same rule applies: rightward movement means greater value. Whether positive or negative, the number line order never changes.

Number Line Comparison with Negative Values

$B > A$

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Understand the problem

$B > A$

Step-by-step solution

We begin by locating the numerical representation of the letter on the number line:

$B=-4$

$A=-5$

We then substitute the letters B and A with their numerical value :

$-4 > -5$

To conclude we can determine that the answer is indeed correct.

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Rule: Numbers increase in value moving right on number line
Technique: Compare positions: $B(-4)$ is right of $A(-5)$ , so $-4 > -5$
Check: Verify by substitution: $-4 > -5$ equals $B > A$ ✓

Common Mistakes

Avoid these frequent errors

Thinking larger negative numbers are greater
Don't assume -5 > -4 because 5 > 4 in positive numbers = wrong comparison! Negative numbers follow opposite order: the closer to zero, the larger. Always remember that -1 > -2 > -3 > -4 > -5.

Practice Quiz

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FAQ

Everything you need to know about this question

Why is -4 greater than -5 if 5 is bigger than 4?

Think of negative numbers as debt! Having $4 in debt is better than having $5 in debt. On a number line, moving right always means getting bigger, regardless of positive or negative.

How do I remember the order of negative numbers?

Use the temperature trick: -4°F is warmer (greater) than -5°F. The closer a negative number is to zero, the larger it is!

What if the letters were in different positions?

Always locate each letter's numerical value first, then compare those numbers. The physical position on the number line tells you everything you need to know.

Can I just look at the number line without finding exact values?

Yes! Since B is to the right of A on the number line, B must be greater than A. Moving right always means increasing value.

What if both numbers were positive?

The same rule applies: rightward movement means greater value. Whether positive or negative, the number line order never changes.

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