Solve the Inequality Expression: ?:+39:+409<0

Q: How do I know what sign the answer should have?

Look at the inequality symbol! Since we need something less than zero (\( ), the final result must be negative.

Q: Why can't the answer be a positive number?

Because the problem asks for a result that is less than zero. Positive numbers like +1 or +905 are greater than zero, so they don't satisfy the inequality.

Q: What happens when I divide negative by positive?

When you divide a negative number by a positive number, you always get a negative result. This rule helps you determine the correct sign pattern!

Q: How do I check if -98 is the right answer?

Substitute -98 into the expression: $ -98 \div 39 \div 409 $ gives you a negative number, and negative numbers are indeed less than zero!

Q: What if I'm confused about the division order?

Work from left to right! First divide the mystery number by 39, then divide that result by 409. The key is making sure your starting number gives a negative final result.

Division Sign Patterns with Inequality Solutions

$?:+39:+409<0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the unknown

00:13 Positive divided by positive is always positive

00:21 Let's assume the unknown is positive, the answer will be greater than 0

00:31 Therefore the unknown must be negative

00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$?:+39:+409<0$

Step-by-step solution

Let's pay attention to the exercise on the left side in terms of plus and minus signs.

The exercise looks like this:

$?:+:+=$

If we solve the equation from left to right, we can see that we first divide a number by a positive number:

$?:+=$

If we use a positive number, we'll get a positive number, and then in the next exercise, dividing a positive number by a positive number would result in a number greater than zero.

Therefore, we need to divide a negative number by a positive number in order to get a negative number.

Therefore:

$-:+=-$

$- < 0$

Therefore the answer is $-98$

Final Answer

$-98$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by positive equals negative result
Technique: Test $-98 \div 39 \div 409 = -\frac{98}{15951}$ which is negative
Check: Verify the result is less than zero: $-\frac{98}{15951} < 0$ ✓

Common Mistakes

Avoid these frequent errors

Choosing positive numbers for division patterns
Don't pick positive numbers like +1 or +905 when you need a negative result = positive ÷ positive = positive! This gives a positive answer that cannot be less than zero. Always choose a negative starting number to ensure the final result is negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

How do I know what sign the answer should have?

Look at the inequality symbol! Since we need something less than zero ( $< 0$ ), the final result must be negative.

Why can't the answer be a positive number?

Because the problem asks for a result that is less than zero. Positive numbers like +1 or +905 are greater than zero, so they don't satisfy the inequality.

What happens when I divide negative by positive?

When you divide a negative number by a positive number, you always get a negative result. This rule helps you determine the correct sign pattern!

How do I check if -98 is the right answer?

Substitute -98 into the expression: $-98 \div 39 \div 409$ gives you a negative number, and negative numbers are indeed less than zero!

What if I'm confused about the division order?

Work from left to right! First divide the mystery number by 39, then divide that result by 409. The key is making sure your starting number gives a negative final result.

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