Solve: (-4)+2+(-3)□5 - Finding the Missing Operator

Integer Operations with Comparison Symbols

Fill in the missing sign (?):

(4)+2+(3)?5 (-4)+2+(-3)\text{?}5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:04 Let's start from point (-4) on the negative side of the axis
00:07 The number is oriented, positive
00:12 The positive direction on the axis is right, so we'll take 2 to the right
00:20 The number is oriented, negative
00:24 The negative direction on the axis is left, so we'll take 3 to the left
00:39 This is the solution for the left side
00:44 The further right the number is on the axis, the larger it is
00:46 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

Fill in the missing sign (?):

(4)+2+(3)?5 (-4)+2+(-3)\text{?}5

2

Step-by-step solution

First let's solve the equation:

(4)+2+(3)= (-4)+2+(-3)=

We'll locate -4 on the number line and move two steps to the right (since 2 is greater than zero):

-11-10-9-8-7-6-5-4-3-2-101

This takes us to the number -2.

Now let's move three steps to the left (since minus 3 is less than zero):

-11-10-9-8-7-6-5-4-3-2-101

This takes us to -5.

The solution to the equation is:

(4)+2+(3)=5 (-4)+2+(-3)=-5

Therefore, since 5 5 is greater than 5 -5 , the missing sign must be: < < .

3

Final Answer

< <

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Calculate left side first, then compare to right side
  • Technique: Use number line: (-4) + 2 + (-3) = -5
  • Check: Verify that -5 < 5 by locating both numbers on number line ✓

Common Mistakes

Avoid these frequent errors
  • Comparing before calculating the left side
    Don't compare (-4) + 2 + (-3) directly to 5 without calculating = wrong comparison! You must first solve the left side completely to get -5, then compare -5 to 5. Always calculate the expression first, then determine the relationship.

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 solve the left side first?

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You must simplify the expression before comparing! Just like in regular equations, you can't compare a complex expression to a number without knowing what that expression equals.

How do I add negative numbers on a number line?

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Start at the first number, then move right for positive numbers and move left for negative numbers. Adding (-3) means moving 3 steps to the left!

What's the difference between < and > symbols?

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Think of the symbols as hungry mouths that always eat the bigger number! The symbol < < means "less than" and > > means "greater than".

Can I use a calculator for this type of problem?

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Yes, but understanding the number line method helps you visualize negative numbers better. Use a calculator to check your work, but try the number line approach first!

What if I get confused with negative signs?

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  • Adding a negative: Move left on the number line
  • Adding a positive: Move right on the number line
  • Remember: (-4) + 2 means start at -4, then move 2 steps right

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