Evaluate the arithmetic expression 8(6 + 5) − 10 and choose the correct numerical value.

Introduction / Context:
This problem checks your understanding of the order of operations, often remembered by the rule BODMAS or PEMDAS. You must correctly handle brackets or parentheses, multiplication, and subtraction in the expression 8(6 + 5) − 10. Many errors come from doing operations in the wrong order or making small arithmetic mistakes.

Given Data / Assumptions:

• The expression is 8(6 + 5) − 10.
• There is a pair of parentheses around 6 + 5.
• The term 8(6 + 5) means 8 multiplied by the result inside the parentheses.
• We subtract 10 at the end.
• All operations are ordinary integer arithmetic.

Concept / Approach:
The order of operations tells us to compute parentheses first, then multiplication or division, and finally addition or subtraction. So we must first add 6 and 5, then multiply by 8, and finally subtract 10. This systematic approach prevents mistakes that come from working left to right without regard to operation priority.

Step-by-Step Solution:
Step 1: Evaluate the expression inside the parentheses: 6 + 5. Step 2: Compute 6 + 5 = 11. Step 3: Now the expression becomes 8 * 11 − 10. Step 4: Perform the multiplication: 8 * 11 = 88. Step 5: Now subtract 10 from 88: 88 − 10 = 78. Step 6: Therefore, the value of the expression is 78.

Verification / Alternative check:
You can quickly verify your answer by doing the calculation again in a slightly different layout. For example, note that 8 * (6 + 5) is 8 * 11, and 8 * 10 is 80, while 8 * 1 is 8, so 80 + 8 = 88. Subtracting 10 then gives 78. Using mental arithmetic in two ways that agree gives confidence in the result.

Why Other Options Are Wrong:

• 76: This might come from subtracting 12 instead of 10 or miscomputing the multiplication.
• 80: This could result from adding 6 and 5 to get 11, but then mistakenly using 10 * 8 instead of 11 * 8.
• 82: This may be the result of 8 * 11 = 88 and then subtracting 6 instead of 10.
• 68: This could arise from computing 6 + 5 = 11, then doing 6 * 8 = 48, adding 5 to get 53, and then subtracting 10, which ignores the correct grouping.

Common Pitfalls:
A very common mistake is to start multiplying 8 by 6 before dealing with the entire bracket, which violates the order of operations. Another pitfall is careless subtraction at the final step. Writing each step clearly and respecting parentheses prevents these simple but costly errors in timed tests.

Final Answer:
The correct value of the expression 8(6 + 5) − 10 is 78.