Solving E < C: Number Line Position Comparison Problem

Q: Why is -1 greater than -3 if 3 is bigger than 1?

With negative numbers, the rules flip! Think of it like temperature: -1°C is warmer than -3°C. On a number line, numbers get smaller as you move left from zero.

Q: How do I remember which negative number is bigger?

Use the number line trick: whichever negative number is closer to zero is the larger number. So -1 is bigger than -3 because -1 is only 1 step from zero!

Q: What if I can't see the number line clearly?

Look for the numerical labels below each point. Match each letter to its number, then compare the actual values like $ -1 $ and $ -3 $.

Q: Can I use this method for any inequality on a number line?

Absolutely! Always: Find the numerical value for each letterSubstitute into the inequalityCheck if the statement is true or false

Q: What does it mean when the inequality is 'Not true'?

It means the mathematical statement is false. In this case, \( E becomes \( -1 , which is incorrect because -1 is actually greater than -3.

Number Line Inequalities with Negative Numbers

$E < C$

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Understand the problem

$E < C$

Step-by-step solution

Let's begin by locating the numerical representation of the letters on the number line:

$E=-1$

$C=-3$

Now let's insert the numerical values of the letters in order to test the expression:

$-1 < -3$

It appears that the answer is not correct.

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Reading Number Lines: Find exact positions by matching letters to numerical values
Technique: E is at -1, C is at -3, so test -1 < -3
Check: On number line, -1 is right of -3, so -1 > -3 ✓

Common Mistakes

Avoid these frequent errors

Confusing position with value for negative numbers
Don't assume larger position means larger value with negatives = wrong inequality! Numbers further left are actually smaller. Always remember -1 is greater than -3 because -1 is closer to zero.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

Why is -1 greater than -3 if 3 is bigger than 1?

With negative numbers, the rules flip! Think of it like temperature: -1°C is warmer than -3°C. On a number line, numbers get smaller as you move left from zero.

How do I remember which negative number is bigger?

Use the number line trick: whichever negative number is closer to zero is the larger number. So -1 is bigger than -3 because -1 is only 1 step from zero!

What if I can't see the number line clearly?

Look for the numerical labels below each point. Match each letter to its number, then compare the actual values like $-1$ and $-3$ .

Can I use this method for any inequality on a number line?

Absolutely! Always:

Find the numerical value for each letter
Substitute into the inequality
Check if the statement is true or false

What does it mean when the inequality is 'Not true'?

It means the mathematical statement is false. In this case, $E < C$ becomes $-1 < -3$ , which is incorrect because -1 is actually greater than -3.

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