Solve the Equation: Finding the Missing Number in ? - 4.3 = 8.2

Q: Why do I add 4.3 when the equation shows subtraction?

Great question! When you see $ ? - 4.3 $, you need to undo that subtraction. The opposite of subtracting 4.3 is adding 4.3, which cancels it out completely.

Q: What if I accidentally subtract 4.3 from both sides?

You'll get the wrong answer! $ 8.2 - 4.3 = 3.9 $, not 12.5. Remember: to isolate the variable, you must reverse the operation, not repeat it.

Q: How can I check if 12.5 is really correct?

Simple! Replace the ? with 12.5 in the original equation: $ 12.5 - 4.3 = 8.2 $. Since this is true, your answer is correct!

Q: Do I always add to both sides when there's subtraction?

Yes! When you see $ x - \text{number} $, always add that number to both sides. This is the fundamental rule for solving equations with subtraction.

Linear Equations with Decimal Subtraction

Fill in the missing value (?):

$?-4.3=8.2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct answer

00:04 Let's write down each option and check

00:17 We'll use long subtraction for calculation

00:24 Let's calculate and substitute

00:47 We see that the first option doesn't fit, let's move to the second

00:54 Again we'll use the same method and check

01:06 Let's calculate and substitute

01:40 We see that the second option doesn't fit, let's move to the third

01:47 Again we'll use the same method and check

01:52 Let's calculate and substitute

02:29 We see that the third option fits, let's move to the fourth

02:37 Again we'll use the same method and check

02:44 Let's calculate and substitute

03:13 We see that the fourth option doesn't fit

03:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing value (?):

$?-4.3=8.2$

Step-by-step solution

To solve the equation $? - 4.3 = 8.2$ , we will isolate the variable $?$ .

Step 1: Add 4.3 to both sides of the equation to eliminate the subtraction from the left-hand side:

$\begin{aligned} ? - 4.3 + 4.3 &= 8.2 + 4.3 \\ ? &= 12.5 \end{aligned}$

Therefore, the solution to the problem is $\boxed{12.5}$ .

Final Answer

12.5

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Add same value to both sides to eliminate subtraction
Technique: Add 4.3 to both sides: 8.2 + 4.3 = 12.5
Check: Substitute back: 12.5 - 4.3 = 8.2 ✓

Common Mistakes

Avoid these frequent errors

Subtracting 4.3 from both sides instead of adding
Don't subtract 4.3 from both sides when you see ? - 4.3 = 8.2 - 4.3 = 3.9! This makes the equation harder by creating more subtraction. Always add 4.3 to both sides to cancel out the -4.3 on the left.

Practice Quiz

Test your knowledge with interactive questions

$\text{0.6+0}.5=$

FAQ

Everything you need to know about this question

Why do I add 4.3 when the equation shows subtraction?

Great question! When you see $? - 4.3$ , you need to undo that subtraction. The opposite of subtracting 4.3 is adding 4.3, which cancels it out completely.

What if I accidentally subtract 4.3 from both sides?

You'll get the wrong answer! $8.2 - 4.3 = 3.9$ , not 12.5. Remember: to isolate the variable, you must reverse the operation, not repeat it.

How can I check if 12.5 is really correct?

Simple! Replace the ? with 12.5 in the original equation: $12.5 - 4.3 = 8.2$ . Since this is true, your answer is correct!

Do I always add to both sides when there's subtraction?

Yes! When you see $x - \text{number}$ , always add that number to both sides. This is the fundamental rule for solving equations with subtraction.

What if the decimal has more places, like 4.37?

The process is exactly the same! Add 4.37 to both sides. Decimal place values don't change the method, just be careful with your decimal arithmetic.

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