Solve the Equation: 75 - Triangle Symbol = 70

Linear Equations with Symbol Variables

Determine the numerical value of the triangle:

75=70 75-\triangle=70

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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:

75=70 75-\triangle=70

2

Step-by-step solution

To solve the equation 75=70 75 - \triangle = 70 , we need to find the value of \triangle.

We start with the equation:

75=70 75 - \triangle = 70

Our goal is to solve for \triangle. To do this, we isolate \triangle by rearranging the equation:

=7570\triangle = 75 - 70

Next, we perform the subtraction on the right side:

=5\triangle = 5

Therefore, the numerical value of the triangle is =5\triangle = 5.

Thus, the correct answer is choice 4: 5 5 .

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Isolate the unknown by performing inverse operations on both sides
  • Technique: Rearrange 75=70 75 - \triangle = 70 to get =7570=5 \triangle = 75 - 70 = 5
  • Check: Substitute back: 755=70 75 - 5 = 70

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting when isolating the variable
    Don't think 75 - triangle = 70 means triangle = 70 - 75 = -5! This confuses the order of operations and gives negative answers when positive ones are expected. Always move terms carefully: triangle = 75 - 70.

Practice Quiz

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Add fifty units to the number 31.

What is the resulting number?

FAQ

Everything you need to know about this question

Why can't I just subtract 70 from both sides?

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You could subtract 70 from both sides to get 5=0 5 - \triangle = 0 , but then you'd need another step to isolate the triangle. It's more efficient to rearrange directly to =7570 \triangle = 75 - 70 .

What if the triangle symbol confuses me?

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Think of the triangle as just another variable, like x or y! The shape doesn't matter - it's still an unknown number you need to find using the same algebraic rules.

How do I know which number to subtract from which?

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Look at the original equation structure. Since it's 75=70 75 - \triangle = 70 , you need 75 minus something equals 70. That something is 75 - 70 = 5.

Can I solve this by adding triangle to both sides instead?

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Yes! Adding \triangle to both sides gives 75=70+ 75 = 70 + \triangle , then subtract 70 from both sides to get =5 \triangle = 5 . Same answer, different path!

What if I get a different answer choice?

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Always check your work! Substitute your answer back into the original equation. If 75your answer70 75 - \text{your answer} \neq 70 , then review your steps and try again.

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