Verified Answer :

  • Simplify the expression by applying the rule of signs \(-(-x) = +x\): \(-27 - (-39) - (-34) = -27 + 39 + 34\).
  • Combine the terms: \(-27 + 39 = 12\).
  • Add the final constant: \(12 + 34 = 46\).
  • The final result is \(\boxed{46}\).

Explanation

  1. Problem Analysis

We are presented with the arithmetic expression \(-27 - (-39) - (-34)\). This problem involves understanding the rules of signs when subtracting negative integers. Recall that subtracting a negative number is equivalent to adding its positive counterpart, expressed by the rule \(-(-x) = +x\). Our goal is to evaluate this expression systematically.

  1. Applying the Rule of Signs

Using the property \(-(-x) = +x\), we can simplify each subtraction of a negative number. The expression \(-27 - (-39) - (-34)\) becomes \(-27 + 39 + 34\). This rewriting eliminates the parentheses and transforms the expression into a simpler addition problem.

  1. Final Calculation

Now we perform the addition from left to right: first, compute \(-27 + 39\), which equals \(12\). Next, add the remaining term: \(12 + 34 = 46\). Thus, the final value of the expression is \(46\).

Examples

Think of your bank balance as an example. If you start with a balance of \(\$-27\) (representing a debt), and then you receive a credit of \(\$39\) followed by another credit of \(\$34\), you are essentially performing the calculation \(-27 + 39 + 34\). This simple arithmetic helps in tracking changes in your finances when dealing with debts and income!

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