Solve the following equation


7+84÷(−2)×(14−(−8))


Let's solve the equation step by step:

Given equation:
\[
7 + \frac{84}{-2} \times (14 - (-8))
\]

### Step 1: Simplify inside the parentheses
\[
14 - (-8) = 14 + 8 = 22
\]
Now the equation becomes:
\[
7 + \frac{84}{-2} \times 22
\]

### Step 2: Perform the division
\[
\frac{84}{-2} = -42
\]
Now the equation is:
\[
7 + (-42) \times 22
\]

### Step 3: Perform the multiplication
\[
-42 \times 22 = -924
\]
Now the equation is:
\[
7 + (-924) = 7 - 924
\]

### Step 4: Perform the addition/subtraction
\[
7 - 924 = -917
\]

Thus, the solution to the equation is:
\[
\boxed{-917}
\]

Would you like more details on any step, or do you have any questions?

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Here are 8 related questions you might find useful:
1. How do you simplify expressions with nested parentheses?
2. How do you handle negative numbers in multiplication?
3. What are the rules for division with negative numbers?
4. How does the order of operations affect solving equations?
5. Can you explain the distributive property in more detail?
6. How do you add and subtract negative numbers?
7. What are the properties of multiplication and division with negatives?
8. How can parentheses change the result of an expression?

**Tip**: Always remember to follow the order of operations (PEMDAS) when solving complex equations!

Learn how to solve the equation 7 + 84 ÷ (-2) × (14 - (-8)) with a detailed step-by-step solution. This problem involves applying the order of operations and integer operations, including division and multiplication with negative numbers. Suitable for students in Grades 7-9.

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