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

Add fifty units to the number 31.

What is the resulting number?

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?

+

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?

+

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?

+

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?

+

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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