Verified Answer :

  • Identify that subtracting a negative number is equivalent to addition: \(-2 - (-4) = -2 + 4\).
  • Recognize that adding a negative number is equivalent to subtraction: \(-2 + 4 + (-18) = -2 + 4 - 18\).
  • Calculate the result step-by-step: \(-2 + 4 = 2\), and \(2 - 18 = -16\).
  • The final result is \(\boxed{-16}\).

Explanation

  1. Analyzing the Expression and Rules

We are given the expression \(-2 - (-4) + (-18)\). To simplify this, we need to apply the fundamental rules of arithmetic regarding the signs of integers:

  1. Subtracting a negative number is equivalent to adding its positive counterpart: \(a - (-b) = a + b\).
  2. Adding a negative number is equivalent to subtracting its positive counterpart: \(a + (-b) = a - b\).

These rules allow us to rewrite the expression with standard addition and subtraction operations, making it much easier to evaluate.

  1. Performing the Calculations

Now we apply the rules identified in the first step to rewrite the expression:

  • For the term \(-(-4)\), the subtraction of a negative value becomes addition: \(-(-4) = +4\).
  • For the term \(+(-18)\), adding a negative value becomes subtraction: \(+(-18) = -18\).

Substituting these into our original expression, we get:
\(-2 + 4 - 18\)

Now, we perform the operations sequentially from left to right:

  • First, \(-2 + 4 = 2\).
  • Next, we take this result and subtract 18: \(2 - 18 = -16\).
  1. Final Result

After applying the arithmetic rules and performing the sequence of additions and subtractions, we have determined that \(-2 - (-4) + (-18) = -16\). The final simplified value is \(\boxed{-16}\).

Examples

Think of this calculation in terms of a bank account balance. If you start with a debt of \(\$2\) (\(-2\)), and then you receive a refund of \(\$4\) (\(-(-4)\)), your balance increases. However, if you then have a recurring monthly fee of \(\$18\) (\(+(-18)\)), your total balance decreases. By following the order of operations, you can track your net balance, which in this case leads to a total debt of \(\$16\), or \(\boxed{-16}\). This illustrates how tracking positive and negative values is essential for managing personal finances effectively.

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