Solve the Equation: Finding the Number That Minus (-12) Equals -40

Q: Why does minus a negative number become addition?

Think of it like this: taking away a debt is the same as gaining money! When you subtract a negative number, you're removing something that was already negative, which makes the result more positive.

Q: How do I remember the double negative rule?

Use this phrase: "Two negatives make a positive!" Just like in English grammar, double negatives cancel each other out and become positive in math too.

Q: What if I forgot to change the sign and solved ? - 12 = -40?

You'd get ? = -28, which is wrong! Always check your answer by substituting back: -28 - (-12) = -28 + 12 = -16, not -40.

Q: Can I solve this equation a different way?

Yes! You could add -12 to both sides directly: $ ? - (-12) + (-12) = -40 + (-12) $. But converting the double negative first is usually clearer and less confusing.

Q: Why is the answer negative when we're adding 12?

Remember, we need ? + 12 = -40. Since we're adding 12 to get -40, the original number must be even more negative than -40. That's why ? = -52!

Linear Equations with Negative Sign Operations

Solve the following expression:

$\text{?}-(-12)=-40$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Negative times negative always equals positive

00:07 Open parentheses

00:14 Isolate the unknown

00:32 Calculate each operation separately

00:47 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 expression:

$\text{?}-(-12)=-40$

Step-by-step solution

Note the following rule:

$-(-x)=+$

We must rewrite the exercise in the appropriate form:

$?+12=-40$

Next, we will add -12 to both sides to cancel out the left side:

$?+12-12=-40-12$

This leaves us with:

$?+0=-52$

$?=-52$

Final Answer

$-52$

Key Points to Remember

Essential concepts to master this topic

Rule: Double negative becomes positive: $-(-x) = +x$
Technique: Rewrite ? - (-12) = -40 as ? + 12 = -40
Check: Substitute -52: -52 - (-12) = -52 + 12 = -40 ✓

Common Mistakes

Avoid these frequent errors

Treating minus negative as subtraction
Don't keep ? - (-12) as subtraction = wrong setup! This ignores the double negative rule and leads to ? - 12 = -40, giving ? = -28 instead of -52. Always convert minus negative to addition first.

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 does minus a negative number become addition?

Think of it like this: taking away a debt is the same as gaining money! When you subtract a negative number, you're removing something that was already negative, which makes the result more positive.

How do I remember the double negative rule?

Use this phrase: "Two negatives make a positive!" Just like in English grammar, double negatives cancel each other out and become positive in math too.

What if I forgot to change the sign and solved ? - 12 = -40?

You'd get ? = -28, which is wrong! Always check your answer by substituting back: -28 - (-12) = -28 + 12 = -16, not -40.

Can I solve this equation a different way?

Yes! You could add -12 to both sides directly: $? - (-12) + (-12) = -40 + (-12)$ . But converting the double negative first is usually clearer and less confusing.

Why is the answer negative when we're adding 12?

Remember, we need ? + 12 = -40. Since we're adding 12 to get -40, the original number must be even more negative than -40. That's why ? = -52!

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