Solve the Integer Equation: -30-(-2)+(-8)+5

Q: Why does minus a negative become positive?

Think of it like owing a debt: if someone takes away your debt of $2, you actually gain $2! Mathematically, $ -(-2) = +2 $ because two negatives cancel out.

Q: Should I work left to right or handle negatives first?

Handle double negatives first, then work left to right. Convert $ -(-2) $ to $ +2 $, then compute: $ -30 + 2 + (-8) + 5 $.

Q: How do I add negative numbers on a number line?

Start at your first number, then move left for negative additions and move right for positive additions. Each step represents one unit of movement.

Q: What's the difference between -8 and (-8)?

There's no difference! Both represent negative eight. The parentheses in $ +(-8) $ just make it clear we're adding a negative number.

Q: Can I group positive and negative numbers separately?

Yes! Positives: $ 2 + 5 = 7 $. Negatives: $ -30 + (-8) = -38 $. Then combine: $ 7 + (-38) = -31 $.

Integer Operations with Negative Signs

Solve the following equation:

$-30-(-2)+(-8)+5=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Negative times negative always equals positive

00:07 Open parentheses

00:13 Take 2 jumps right (to the positive side) on the axis

00:22 This is the solution to the operation

00:33 Take 8 jumps left (to the negative side) on the axis

00:46 This is the solution to the operation

01:00 Take 5 jumps right (to the positive side) on the axis

01:20 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 equation:

$-30-(-2)+(-8)+5=$

Step-by-step solution

Let's begin by applying the following rule in order to rewrite the equation:

$-(-x)=+$

$-30+2+(-8)+5=$

$-28+(-8)+5=$

Next we will locate negative 28 on the number line and proceed 8 steps to the left (since negative 8 is less than zero):

We reach negative 36.

Resulting in the following exercise:

$-36+5=$

Next we locate negative 36 on the number line and proceed 5 steps to the right (since 5 is greater than zero):

We reach negative 31

Final Answer

$-31$

Key Points to Remember

Essential concepts to master this topic

Double Negative Rule: Subtracting a negative number means addition
Technique: Convert $-(-2)$ to $+2$ then compute left to right
Check: $-30 + 2 - 8 + 5 = -31$ matches our answer ✓

Common Mistakes

Avoid these frequent errors

Treating double negatives as subtraction
Don't compute -(-2) as -2 = gives -38 instead of -31! This ignores the rule that subtracting a negative equals adding a positive. Always change -(-x) to +x before calculating.

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

Why does minus a negative become positive?

Think of it like owing a debt: if someone takes away your debt of $2, you actually <em>gain</em>$ 2! Mathematically, $-(-2) = +2$ because two negatives cancel out.

Should I work left to right or handle negatives first?

Handle double negatives first, then work left to right. Convert $-(-2)$ to $+2$ , then compute: $-30 + 2 + (-8) + 5$ .

How do I add negative numbers on a number line?

Start at your first number, then move left for negative additions and move right for positive additions. Each step represents one unit of movement.

What's the difference between -8 and (-8)?

There's no difference! Both represent negative eight. The parentheses in $+(-8)$ just make it clear we're adding a negative number.

Can I group positive and negative numbers separately?

Yes! Positives: $2 + 5 = 7$ . Negatives: $-30 + (-8) = -38$ . Then combine: $7 + (-38) = -31$ .

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Solve the Integer Equation: -30-(-2)+(-8)+5

Integer Operations with Negative Signs

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does minus a negative become positive?

Should I work left to right or handle negatives first?

How do I add negative numbers on a number line?

What's the difference between -8 and (-8)?

Can I group positive and negative numbers separately?

🌟 Unlock Your Math Potential

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