Solve the Equation: Finding the Unknown in 12-?=15

Q: Why is the answer negative when we're subtracting to get a bigger number?

Great question! When $ 12 - ? = 15 $, we need to subtract something from 12 to get 15. Since 15 is bigger than 12, we must subtract a negative number, which actually adds to 12!

Q: How do I remember the double negative rule?

Think of it like this: subtracting a debt is like gaining money! If you owe someone -$3 (negative debt), and they forgive it, you actually gain $3. So $ 12 - (-3) = 12 + 3 $.

Q: Can I solve this by moving numbers around instead?

Yes! You can rewrite $ 12 - ? = 15 $ as $ 12 - 15 = ? $, which gives you $ -3 = ? $. Both methods work!

Q: What if I got a positive answer like +3?

Let's check: $ 12 - 3 = 9 $, not 15! This shows your answer is wrong. Always substitute back to verify your solution makes the original equation true.

Q: Is this the same as solving 12 + ? = 15?

No! $ 12 + ? = 15 $ gives us $ ? = 3 $ (positive 3), while $ 12 - ? = 15 $ gives us $ ? = -3 $ (negative 3). The operation sign matters!

Subtraction Equations with Negative Unknown

Solve the following problem:

$12-?=15$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Find point (12) on the axis

00:07 Find the desired result (15) on the axis

00:12 Find the number of jumps between the result and starting point

00:17 We can see that the difference is +3

00:26 Negative times negative always equals positive

00:30 Therefore we subtract by (-3)

00:37 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

Solve the following problem:

$12-?=15$

Step-by-step solution

We know that the distance between 12 and 15 is three steps.

In other words:

$12+3=15$

Now let's remember the rule:

$-(-x)=+$

We'll substitute x with the number 3 as follows:

$12-(-3)=15$

Therefore, the answer is minus 3

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Rule: When subtracting a negative number, it becomes addition
Technique: Find the distance first: 12 to 15 is 3 steps
Check: Substitute back: 12 - (-3) = 12 + 3 = 15 ✓

Common Mistakes

Avoid these frequent errors

Forgetting that subtracting negative equals positive
Don't think 12 - x = 15 means x must be positive = wrong answer! This ignores the double negative rule. Always remember that subtracting a negative number becomes addition: 12 - (-3) = 12 + 3.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why is the answer negative when we're subtracting to get a bigger number?

Great question! When $12 - ? = 15$ , we need to subtract something from 12 to get 15. Since 15 is bigger than 12, we must subtract a negative number, which actually adds to 12!

How do I remember the double negative rule?

Think of it like this: subtracting a debt is like gaining money! If you owe someone - $3 (negative debt), and they forgive it, you actually gain$ 3. So $12 - (-3) = 12 + 3$ .

Can I solve this by moving numbers around instead?

Yes! You can rewrite $12 - ? = 15$ as $12 - 15 = ?$ , which gives you $-3 = ?$ . Both methods work!

What if I got a positive answer like +3?

Let's check: $12 - 3 = 9$ , not 15! This shows your answer is wrong. Always substitute back to verify your solution makes the original equation true.

Is this the same as solving 12 + ? = 15?

No! $12 + ? = 15$ gives us $? = 3$ (positive 3), while $12 - ? = 15$ gives us $? = -3$ (negative 3). The operation sign matters!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime