Solve: ⬜-(-3)-(-10)=-40 | Fill in the Missing Value

Q: Why does -(-3) become +3?

The double negative rule says that subtracting a negative number is the same as adding a positive number. Think of it as: "taking away a debt is like gaining money!"

Q: How do I handle multiple double negatives in one problem?

Handle them one at a time. Change each -(-number) to +number, then combine like terms. So $ -(-3)-(-10) $ becomes $ +3+10 = 13 $.

Q: What's the difference between -(+3) and -(-3)?

$ -(+3) = -3 $ (negative of positive 3), but $ -(-3) = +3 $ (negative of negative 3). The sign inside the parentheses matters!

Q: Can I solve this without using the double negative rule?

You could, but it's much harder! The double negative rule simplifies the equation from $ ⬜-(-3)-(-10)=-40 $ to $ ⬜+13=-40 $, making it easier to solve.

Q: How do I check if -53 is really the right answer?

Substitute -53 back into the original equation: $ -53-(-3)-(-10) = -53+3+10 = -40 $. Since this equals -40, our answer is correct!

Algebraic Equations with Double Negative Operations

$⬜-(-3)-(-10)=-40$

Fill in the blank.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 Negative times negative always equals positive

00:09 Open parentheses

00:14 Calculate the operation

00:20 Isolate the unknown

00:36 Calculate each operation separately

00:48 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

$⬜-(-3)-(-10)=-40$

Fill in the blank.

Step-by-step solution

First let's remember the rule:

$-(-x)=+$

Now let's rewrite the exercise like so:

$?+3+10=-40$

$?+13=-40$

Then we can add -13 to both sides to cancel out the left side:

$?+13-13=-40-13$

Finally, we obtain:

$?+0=-53$

$?=-53$

Final Answer

$-53$

Key Points to Remember

Essential concepts to master this topic

Rule: Double negatives become positive: -(-x) = +x
Technique: Rewrite $⬜-(-3)-(-10)=-40$ as $⬜+3+10=-40$
Check: Substitute -53: -53-(-3)-(-10) = -53+3+10 = -40 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when removing parentheses
Don't just remove the parentheses without changing signs = wrong calculation! Writing ⬜-3-10=-40 gives ⬜=-27 instead of -53. Always apply the double negative rule: -(-x) becomes +x.

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 -(-3) become +3?

The double negative rule says that subtracting a negative number is the same as adding a positive number. Think of it as: "taking away a debt is like gaining money!"

How do I handle multiple double negatives in one problem?

Handle them one at a time. Change each -(-number) to +number, then combine like terms. So $-(-3)-(-10)$ becomes $+3+10 = 13$ .

What's the difference between -(+3) and -(-3)?

$-(+3) = -3$ (negative of positive 3), but $-(-3) = +3$ (negative of negative 3). The sign inside the parentheses matters!

Can I solve this without using the double negative rule?

You could, but it's much harder! The double negative rule simplifies the equation from $⬜-(-3)-(-10)=-40$ to $⬜+13=-40$ , making it easier to solve.

How do I check if -53 is really the right answer?

Substitute -53 back into the original equation: $-53-(-3)-(-10) = -53+3+10 = -40$ . Since this equals -40, our answer is correct!

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