Solve the Integer Equation: -3-2+10 Step by Step

Q: Why do we group the negative numbers together first?

Grouping negative numbers helps you see the pattern clearly! When you have -3-2, you're really adding two negative numbers: (-3) + (-2) = -5. Then it's easier to see -5 + 10.

Q: What's the substitution property mentioned in the solution?

The substitution property lets you rewrite problems in easier forms. Here, $ -5+10 $ becomes $ 10-5 $ because adding a negative is the same as subtracting!

Q: How do I know when my final answer should be positive or negative?

Look at the absolute values! Here, you have 5 negative (from -3-2) and 10 positive. Since 10 > 5, your answer is positive. The difference is 10-5 = 5.

Q: Is there a number line trick for this?

Absolutely! Start at 0, move left 3 spaces (-3), left 2 more spaces (-2), now you're at -5. Then move right 10 spaces (+10) to land at positive 5!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve a math problem together.

00:07 First, we'll follow the order of operations.

00:11 We'll work from left to right, step by step.

00:15 We'll arrange the problem to make it easier.

00:18 And that's how we find our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$-3-2+10=$

2

Step-by-step solution

First, we place the subtraction exercise in parentheses, and then we add:

$(-3-2)+10=$

$-5+10=$

We use the substitution property to make solving the exercise easier:

$10-5=5$

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic

Order: Combine negative numbers first, then add positive numbers
Technique: Group negatives: (-3-2) = -5, then -5+10 = 5
Check: Count backward 3, backward 2, forward 10 lands at 5 ✓

Common Mistakes

Avoid these frequent errors

Adding all numbers from left to right without considering signs
Don't just add 3+2+10=15 and worry about signs later = wrong answer! This ignores that subtraction means adding negative numbers. Always treat -3-2 as (-3)+(-2) first, then add the positive number.

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why do we group the negative numbers together first?

+

Grouping negative numbers helps you see the pattern clearly! When you have -3-2, you're really adding two negative numbers: (-3) + (-2) = -5. Then it's easier to see -5 + 10.

Can I just work from left to right instead?

+

Yes, but be careful with signs! Going left to right: -3-2 = -5, then -5+10 = 5. The key is treating each subtraction as adding a negative.

What's the substitution property mentioned in the solution?

+

The substitution property lets you rewrite problems in easier forms. Here, $-5+10$ becomes $10-5$ because adding a negative is the same as subtracting!

How do I know when my final answer should be positive or negative?

+

Look at the absolute values! Here, you have 5 negative (from -3-2) and 10 positive. Since 10 > 5, your answer is positive. The difference is 10-5 = 5.

Is there a number line trick for this?

+

Absolutely! Start at 0, move left 3 spaces (-3), left 2 more spaces (-2), now you're at -5. Then move right 10 spaces (+10) to land at positive 5!

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Solve the Integer Equation: -3-2+10 Step by Step

Integer Addition with Negative Numbers

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