Solve for Triangle Symbol in 8 + △ = 40: Basic Algebra

Linear Equations with Symbol Substitution

Determine the numerical value of the triangle:

If

8+=40 8+\triangle=40

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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:

If

8+=40 8+\triangle=40

2

Step-by-step solution

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

  • Step 1: Identify the given information

  • Step 2: Rearrange the equation to solve for \triangle

  • Step 3: Perform the subtraction to find \triangle

Now, let's work through each step:
Step 1: The problem gives us the equation 8+=40 8 + \triangle = 40 . We need to find the value of \triangle .
Step 2: To isolate \triangle , we subtract 8 from both sides of the equation: =408 \triangle = 40 - 8 .
Step 3: Perform the subtraction, 408=32 40 - 8 = 32 .

Therefore, the solution to the problem is =32 \triangle = 32 .

3

Final Answer

32 32

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Use inverse operations to isolate the unknown symbol
  • Technique: Subtract 8 from both sides: =408=32 \triangle = 40 - 8 = 32
  • Check: Substitute back into original equation: 8+32=40 8 + 32 = 40

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting to isolate the variable
    Don't add 8 to both sides when you see 8 + △ = 40, giving △ = 48! This makes the equation unbalanced because you're doing the same operation that's already there. Always use the opposite operation - subtract 8 from both sides to isolate △.

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 add 8?

+

Because subtraction is the opposite of addition! When you see 8+=40 8 + \triangle = 40 , the 8 is being added to the triangle, so you subtract 8 from both sides to undo that addition.

Can I use different symbols like x instead of the triangle?

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Absolutely! The triangle \triangle is just a symbol representing an unknown number, just like x, y, or any other variable. The solving process stays exactly the same.

What if the equation was triangle + 8 = 40 instead?

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It's the same equation! Addition is commutative, meaning 8+=+8 8 + \triangle = \triangle + 8 . You'd still subtract 8 from both sides to get =32 \triangle = 32 .

How do I check my answer?

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Replace the triangle with your answer in the original equation. If =32 \triangle = 32 , then 8+32=40 8 + 32 = 40 . Since this is true, your answer is correct!

What if I get a negative number as my answer?

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Negative answers are completely normal in algebra! For example, if you had 8+=5 8 + \triangle = 5 , then =3 \triangle = -3 . Just remember to check your work by substituting back.

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