simplify this equation ( ( 100 + ( 14 + 6 ) 2 ) / 50 − 8 + 14 / 2 ) / 3 − 3

Let's break down and simplify the given equation step by step:

$\left( \left( 100 + \left( 14 + 6 \right) 2 \right) / 50 - 8 + 14 / 2 \right) / 3 - 3$

Step 1: Parentheses

First, solve the operation inside the innermost parentheses:

$14 + 6 = 20$

So, the expression becomes:

$\left( \left( 100 + 20 \times 2 \right) / 50 - 8 + 14 / 2 \right) / 3 - 3$

Step 2: Multiplication

Now, perform the multiplication:

$20 \times 2 = 40$

This gives us:

$\left( \left( 100 + 40 \right) / 50 - 8 + 14 / 2 \right) / 3 - 3$

Step 3: Addition

Now, add $100 + 40$:

$100 + 40 = 140$

So, the equation becomes:

$\left( 140 / 50 - 8 + 14 / 2 \right) / 3 - 3$

Step 4: Division

Perform the division:

$140 / 50 = 2.8$

And,

$14 / 2 = 7$

Now, the equation becomes:

$\left( 2.8 - 8 + 7 \right) / 3 - 3$

Step 5: Simplify inside the parentheses

Now, simplify inside the parentheses:

$2.8 - 8 = -5.2$

$-5.2 + 7 = 1.8$

So, the equation becomes:

$\left( 1.8 \right) / 3 - 3$

Step 6: Final Division

Now, divide:

$1.8 / 3 = 0.6$

Step 7: Subtract

Finally, subtract:

$0.6 - 3 = -2.4$

Final Answer:

$\boxed{-2.4}$

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Would you like further explanation or have any questions about the steps? Here are a few related questions you might find helpful:

1. How does the order of operations (PEMDAS) affect simplifying expressions?
2. What is the difference between multiplication and addition in terms of their effect on an equation?
3. How would you simplify an equation with multiple fractions?
4. Can you explain how to deal with negative numbers in operations like subtraction and addition?
5. How do you handle expressions that involve both fractions and parentheses?

Tip: Always start by simplifying inside parentheses first, and then follow the order of operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).