Solve (-12)+(-2)+4?-15: Finding the Missing Number in a Sequence

Integer Operations with Comparison Symbols

(12)+(2)+4?15 (-12)+(-2)+4\text{?}-15

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:03 Let's start from the point (-12) on the negative side of the axis
00:06 The number is directed and negative
00:10 The negative direction on the axis is to the left, so we'll go 2 units left
00:16 The number is directed and positive
00:21 The positive direction on the axis is to the right, so we'll go 4 units right
00:34 This is the solution for the left side
00:44 Let's find both solutions on the axis and see which one is larger
00:47 On the left side, further from point 0 means it's smaller
00:51 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(12)+(2)+4?15 (-12)+(-2)+4\text{?}-15

2

Step-by-step solution

Let's first solve the following equation:

(12)+(2)+4= (-12)+(-2)+4=

We'll then locate -12 on the number line and move two steps to the left (since -2 is less than zero):

-22-21-20-19-18-17-16-15-14-13-12-11-10

This puts us at the number -14.

Now let's move 4 steps to the right (since 4 is greater than zero):

-22-21-20-19-18-17-16-15-14-13-12-11-10

We've reached the number minus 10.

Therefore, the solution to the equation is:

(12)+(2)+4=10 (-12)+(-2)+4=-10

The appropriate sign will be:

10>15 -10>-15

3

Final Answer

> >

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Calculate addition and subtraction from left to right
  • Number Line Method: Start at -12, move left 2 steps, then right 4 steps = -10
  • Comparison Check: Verify that -10 > -15 since -10 is further right on number line ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the order of operations with negative numbers
    Don't calculate (-2) + 4 first to get 2, then (-12) + 2 = -10! This gives the same answer by chance, but breaks mathematical rules. Always work from left to right: (-12) + (-2) = -14, then (-14) + 4 = -10.

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 do I need to work from left to right?

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Addition and subtraction have the same priority in order of operations, so you must work from left to right. This ensures you get the correct answer every time, especially with negative numbers.

How do I know which direction to move on the number line?

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Negative numbers: Move left (towards smaller values)
Positive numbers: Move right (towards larger values)
Think of it as a thermometer - negative goes down, positive goes up!

How do I compare negative numbers?

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On a number line, numbers get larger as you move right. So -10 is greater than -15 because -10 is further to the right. Remember: closer to zero means bigger for negative numbers!

What if I get confused with the signs?

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Use the number line method! It's visual and helps you see exactly where you end up. Start at your first number and follow the moves step by step.

Can I use a calculator for this?

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Yes, but make sure to use parentheses correctly: (-12) + (-2) + 4. Without parentheses, the calculator might interpret -12 + -2 + 4 differently!

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