Solve the Equation: Finding the Missing Number in 12+?+3-1=29

Linear Equations with Missing Addends

12+?+31=29 12+?+3-1=29

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Identify the missing number
00:04 Given that all operations are addition/subtraction
00:07 We may use the commutative property and solve in a different order
00:18 Arrange the exercise in the simplest way possible
00:27 Continue to solve
00:36 Isolate our unknown
00:49 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+?+31=29 12+?+3-1=29

2

Step-by-step solution

To find out which number is missing, we solve the entire exercise to know which number we will have to add to obtain a result of 29:

12+31= 12+3-1=

151=14 15-1=14

To make 14 equal to 29, we will have to add 15.

Let's verify:

2914=15 29-14=15

3

Final Answer

15 15

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Calculate known terms first, then find the missing value
  • Technique: Compute 12 + 3 - 1 = 14, then 29 - 14 = 15
  • Check: Substitute back: 12 + 15 + 3 - 1 = 29 ✓

Common Mistakes

Avoid these frequent errors
  • Trying to solve for the unknown without simplifying known terms first
    Don't randomly guess or work with all terms at once = confusion and wrong answers! This makes the problem much harder than it needs to be. Always combine the known numbers first, then find what's needed to reach the target.

Practice Quiz

Test your knowledge with interactive questions

\( 8 - 2 + 6 = \)

FAQ

Everything you need to know about this question

Why should I calculate the known numbers first?

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Calculating known terms first simplifies the problem! Instead of juggling 4 different numbers, you only need to work with 2: what you have (14) and what you need (29).

What if I get the wrong answer when I check?

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Double-check your arithmetic! Make sure you followed order of operations correctly. Remember: addition and subtraction work left to right when there are no parentheses.

Can I solve this a different way?

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Yes! You could also think of it as 12+?+31=29 12 + ? + 3 - 1 = 29 becoming ?=29123+1 ? = 29 - 12 - 3 + 1 . Both methods give the same answer: 15.

How do I know which operation to use when finding the missing number?

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Think about what makes the equation balanced. If you have 14 and need 29, you must add something. So subtract: 29 - 14 = 15.

What if the missing number was negative?

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That's possible! If your known terms add up to more than the target, the missing number would be negative. The same process works: find the difference.

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