Number Line Inequality: Analyzing Why C > E at Positions -3 and -1

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

Great question! With negative numbers, the rules flip. Think of it like debt: owing $3 is worse than owing $1, so -3

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

Use the number line trick: whichever number is further to the right is always bigger. Since -1 is to the right of -3, we know -1 > -3.

Q: What if I have to compare many negative numbers?

Line them up on a number line or think about their distance from zero. The negative number closest to zero is always the largest negative number.

Q: Does this work for decimals and fractions too?

Absolutely! Whether it's $ -2.5 $ vs $ -1.3 $ or $ -\frac{3}{2} $ vs $ -\frac{1}{2} $, the same rule applies: further right means bigger.

Q: How can I check my comparison is correct?

Try the addition test: if a > b, then a + (positive number) > b + (same positive number). For example, -1 + 5 = 4 and -3 + 5 = 2, and since 4 > 2, we confirm -1 > -3!

Negative Number Comparison on Number Lines

$C > E$

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Understand the problem

$C > E$

Step-by-step solution

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

$C=-3$

$E=-1$

Now let's insert the given values in order to test the expression:

$-3>-1$

It appears that the answer is not correct.

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Rule: On number lines, numbers increase as you move right
Technique: Compare positions: -3 is left of -1, so -3 < -1
Check: Verify -3 > -1 is false since -3 is smaller ✓

Common Mistakes

Avoid these frequent errors

Thinking larger negative numbers are greater
Don't assume -3 > -1 because 3 > 1 = wrong comparison! Negative numbers work opposite to positive numbers. Always remember that -3 is further left on the number line, making it smaller than -1.

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 is -3 smaller than -1 if 3 is bigger than 1?

Great question! With negative numbers, the rules flip. Think of it like debt: owing $3 is <em>worse</em> than owing$ 1, so -3 < -1. The further left on the number line, the smaller the value.

How do I remember which negative number is bigger?

Use the number line trick: whichever number is further to the right is always bigger. Since -1 is to the right of -3, we know -1 > -3.

What if I have to compare many negative numbers?

Line them up on a number line or think about their distance from zero. The negative number closest to zero is always the largest negative number.

Does this work for decimals and fractions too?

Absolutely! Whether it's $-2.5$ vs $-1.3$ or $-\frac{3}{2}$ vs $-\frac{1}{2}$ , the same rule applies: further right means bigger.

How can I check my comparison is correct?

Try the addition test: if a > b, then a + (positive number) > b + (same positive number). For example, -1 + 5 = 4 and -3 + 5 = 2, and since 4 > 2, we confirm -1 > -3!

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