Solve the Equation: Finding the Value in 8 + △ = 68

Basic Algebra with Missing Addends

Determine the numerical value of the triangle:

8+=68 8+{\triangle}=68

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the numerical value of the triangle:

8+=68 8+{\triangle}=68

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Recognize the given equation 8+=68 8 + \triangle = 68 .
  • Step 2: To isolate \triangle , subtract 8 from both sides of the equation.

Now, let's work through each step:
Step 1: We initially have the equation 8+=68 8 + \triangle = 68 .
Step 2: Subtract 8 from both sides to find \triangle :

=688 \triangle = 68 - 8

This calculation gives us:

=60 \triangle = 60

Therefore, the numerical value of the triangle is 60 60 .

3

Final Answer

60 60

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Move numbers to opposite side using inverse operations
  • Subtraction Method: Subtract 8 from both sides: 68 - 8 = 60
  • Verification: Check by substituting: 8 + 60 = 68 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting to isolate the variable
    Don't add 8 to both sides when solving 8 + △ = 68, giving 8 + △ + 8 = 68 + 8! This makes the equation more complex instead of isolating △. Always use the opposite operation - subtract 8 from both sides to get △ = 60.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

Why do I subtract 8 instead of adding 8?

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You need to undo what's being done to the triangle. Since 8 is being added to △, you subtract 8 from both sides to cancel it out and isolate △.

How do I remember which operation to use?

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Think: "What's the opposite?" If you see addition (+), use subtraction (-). If you see subtraction (-), use addition (+). Always do the opposite to both sides!

Can I solve this by guessing and checking?

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Yes, but it's slower! You could try different numbers until 8 + ? = 68, but algebraic solving is faster and more reliable, especially for harder problems.

What if the triangle was on the right side instead?

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Same process! For 68=8+ 68 = 8 + \triangle , you still subtract 8 from both sides: 688= 68 - 8 = \triangle , so =60 \triangle = 60 .

How can I check if my answer is definitely correct?

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Substitute your answer back into the original equation. Replace △ with 60: does 8 + 60 = 68? Yes! If both sides equal the same number, you're right.

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