Solve for the Missing Number in 17-?+4=5: Step-by-Step Guide

Linear Equations with Unknown Middle Terms

17?+4=5 17-?+4=5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Identify the missing value
00:03 Given that there are only addition/subtraction operations
00:06 Use the commutative property and solve in a different order
00:10 Continue to solve the rest of the expression
00:24 Let's isolate our unknown
00:49 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

17?+4=5 17-?+4=5

2

Step-by-step solution

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

We arrange the exercise to isolate the question mark:

17+4?=5 17+4-?=5

We reduce:

21?=5 21-?=5

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

21=?+5 21=?+5

We move the 5 to the other side and change to the correct sign: 215=? 21-5=\text{?}

16=? 16=\text{?}

3

Final Answer

16 16

Key Points to Remember

Essential concepts to master this topic
  • Arrangement: Rearrange terms to isolate the unknown variable systematically
  • Technique: Combine like terms first: 17 + 4 = 21, then solve 21 - ? = 5
  • Check: Substitute back into original equation: 17 - 16 + 4 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Solving without proper rearrangement
    Don't try to solve 17 - ? + 4 = 5 directly without rearranging = confusing order of operations! This leads to sign errors and wrong calculations. Always rearrange to group like terms first, then isolate the variable.

Practice Quiz

Test your knowledge with interactive questions

\( 8 - 2 + 6 = \)

FAQ

Everything you need to know about this question

Why do I need to rearrange the equation first?

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Rearranging helps you combine like terms and see the problem more clearly. Instead of working with 17 - ? + 4 = 5, you get the simpler form 21 - ? = 5.

What if I move terms to the wrong side?

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Remember the golden rule: when you move a term across the equals sign, change its sign. If you move +4, it becomes -4 on the other side.

Can I solve this equation differently?

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Yes! You could also think of it as 17+4?=5 17 + 4 - ? = 5 , which gives 21?=5 21 - ? = 5 . Multiple approaches can work as long as you follow algebraic rules.

How do I know which number to substitute for the question mark?

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The question mark represents the unknown value we're solving for. Once you find that ? = 16, substitute 16 wherever you see the question mark.

What does it mean to 'change the sign' when moving terms?

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When you move a term across the equals sign, it becomes its opposite operation. Addition becomes subtraction, and subtraction becomes addition. This keeps the equation balanced!

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