Solve for the Missing Number: 7-?+4+2×18=29 Using Order of Operations

Missing Variables with Order of Operations

7?+4+2×18=29 7-?+4+2\times18=29

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the exercise and isolate the unknown
00:02 Multiplication comes before addition and subtraction
00:50 Subtract 47 from both sides of the equation in order to isolate the unknown
01:08 Multiply by minus 1 to make the unknown positive

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7?+4+2×18=29 7-?+4+2\times18=29

2

Step-by-step solution

First, we place the multiplication exercise in parentheses:

7?+4+(2×18)=29 7-?+4+(2\times18)=29

We solve the exercise in parentheses:

2×18=36 2\times18=36

Now we obtain the exercise:

7?+4+36=29 7-?+4+36=29

We reduce the addition exercise:

36+4=40 36+4=40

Now we obtain the exercise:

7?+40=29 7-?+40=29

The question mark is the unknown, therefore we will refer to the exercise as an equation.

We arrange the exercise to isolate the question mark:

40+7?=29 40+7-?=29

We reduce:

47?=29 47-?=29

We move 47 to the other side and change to the correct sign:

?=2947 -?=29-47

?=18 -?=-18

We divide both sides by -1 to change to the correct sign:

?=18 ?=18

3

Final Answer

18 18

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Solve multiplication first, then work left to right
  • Technique: Calculate 2×18=36 2\times18 = 36 before adding or subtracting
  • Check: Substitute 18 back: 718+4+36=29 7-18+4+36 = 29

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations and working left to right
    Don't solve 7-?+4 first then multiply = wrong sequence! This ignores PEMDAS and gives incorrect results. Always multiply 2×18 = 36 first, then work with addition and subtraction from left to right.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{6}{3}\times1=\text{ ?} \)

FAQ

Everything you need to know about this question

Why can't I just work from left to right like reading?

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Mathematics has a specific order of operations (PEMDAS)! Multiplication and division must be done before addition and subtraction, regardless of position in the equation.

How do I know which operation to do first?

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Remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In this problem, 2×18 2\times18 comes first!

What if I get a negative number for the missing value?

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That's totally possible! Don't worry if your answer is negative. Just make sure you follow the order of operations correctly and check your work by substituting back.

Can I solve this without using algebra?

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While you could guess and check, using algebraic steps is more reliable. Treat the ? as a variable, follow order of operations, then isolate it step by step.

How do I check if my answer is correct?

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Substitute your answer back into the original equation: 718+4+2×18 7-18+4+2\times18 . If it equals 29, you're right!

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