Solve the Equation: Finding the Value in 8 + Triangle = 30

Linear Equations with Unknown Variables

Determine the numerical value of the triangle:

If

8+=30 8+\triangle=30

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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+=30 8+\triangle=30

2

Step-by-step solution

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

  • Step 1: Set up the equation.
  • Step 2: Isolate the triangle symbol using subtraction.
  • Step 3: Calculate the numerical value of the triangle.

Now, let's work through each step:

Step 1: Set up the equation:

We start with the equation 8+=308 + \triangle = 30.

Step 2: Isolate the triangle symbol:

To find \triangle, we subtract 88 from both sides of the equation:

=308 \triangle = 30 - 8

Step 3: Calculate the numerical value of the triangle:

Performing the subtraction gives us:

=22 \triangle = 22

Therefore, the solution to the problem is =22 \triangle = 22 .

3

Final Answer

22 22

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Use inverse operations to isolate the unknown variable
  • Technique: Subtract 8 from both sides: =308=22 \triangle = 30 - 8 = 22
  • Check: Substitute back into original equation: 8+22=30 8 + 22 = 30

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting to isolate the variable
    Don't add 8 to both sides to get =30+8=38 \triangle = 30 + 8 = 38 ! This makes the equation unbalanced since you're doing the same operation that's already in the equation. Always use the inverse operation - subtract 8 from both sides to isolate the triangle.

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 8 is being added to the triangle, you need to do the opposite operation (subtraction) to cancel it out. Think of it as undoing what's already there!

What if the triangle was on the right side of the equation?

+

The process is exactly the same! Whether it's 8+=30 8 + \triangle = 30 or 30=8+ 30 = 8 + \triangle , you still subtract 8 from both sides to isolate the triangle.

How do I know if I should add or subtract?

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Look at what operation is being done to your variable. If something is being added to it, subtract that number. If something is being subtracted from it, add that number back.

Can I solve this problem by guessing and checking?

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While guessing might work for simple problems, learning the algebraic method is much more reliable and efficient, especially for harder equations you'll encounter later!

What does the triangle symbol represent?

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The triangle \triangle is just a placeholder for an unknown number, like using x or any other letter. It represents the value we need to find.

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