Simplify by using the order of operations.
$-|-5-5|-(-5-5)=$
Answer (2)
The expression − ∣ − 5 − 5∣ − ( − 5 − 5 ) simplifies to 0 by following the order of operations, evaluating the absolute values, and performing the arithmetic calculations correctly. After carrying out each step, we find that the final answer is 0 .
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Simplify inside the absolute value: − 5 − 5 = − 10 .
Evaluate the absolute value: ∣ − 10∣ = 10 .
Simplify inside the parenthesis: − 5 − 5 = − 10 .
Evaluate the expression: − 10 − ( − 10 ) = − 10 + 10 = 0 . The final answer is 0 .
Explanation
Understanding the Expression We are asked to simplify the expression − ∣ − 5 − 5∣ − ( − 5 − 5 ) = using the order of operations. This involves dealing with absolute values, subtraction, and negative signs. Let's break it down step by step.
Simplifying Inside Absolute Value First, we simplify the expression inside the absolute value: − 5 − 5 = − 10 . So, we have − ∣ − 10∣ − ( − 5 − 5 ) .
Evaluating Absolute Value Next, we evaluate the absolute value: ∣ − 10∣ = 10 . Now the expression becomes − 10 − ( − 5 − 5 ) .
Simplifying Inside Parenthesis Now, we simplify the expression inside the parenthesis: − 5 − 5 = − 10 . The expression is now − 10 − ( − 10 ) .
Removing Parenthesis Finally, we deal with the negative sign outside the parenthesis: − ( − 10 ) = 10 . So the expression becomes − 10 + 10 .
Final Calculation Combining the terms, we have − 10 + 10 = 0 . Therefore, the simplified expression is 0 .
Examples
In real life, this type of calculation can be used in scenarios involving gains and losses. For example, imagine you have a debt of $5, and then you incur another debt of $5. This is represented as -5-5 = -10. The absolute value represents the total amount of debt, which is $10. If you then have a negative of this debt, -(-10), it means you are cancelling the debt, resulting in a gain of $10. So, if you initially had a debt of $10 and then gained $10, your net worth becomes $0. This illustrates how simplifying expressions with absolute values and negative signs can help in understanding financial transactions and balances.
