Verified Answer :

  • Combine the first two integers: \(-9 + (-12) = -21\).
  • Add the third integer to the result: \(-21 + 24 = 3\).
  • The final result of the expression \(-9 + (-12) + 24\) is \(\boxed{3}\).

Explanation

  1. Problem Analysis

The problem asks for the numerical value of the expression \(-9 + (-12) + 24\). This is an exercise in basic integer arithmetic involving both negative and positive numbers. We will solve this by performing the addition step-by-step from left to right.

  1. Calculating the Sum of the First Two Terms

First, we combine the first two terms in the expression: \(-9 + (-12)\). When adding two negative numbers, we add their absolute values and keep the negative sign. Thus, \(|-9| + |-12| = 9 + 12 = 21\), and so \(-9 + (-12) = -21\).

  1. Final Calculation

Now, we add the result from the previous step to the final term: \(-21 + 24\). Since the numbers have opposite signs, we subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value. We have \(|24| - |-21| = 24 - 21 = 3\). Since \(|24| > |-21|\), the result is positive. Therefore, \(-21 + 24 = 3\).

  1. Final Answer

The final value of the expression \(-9 + (-12) + 24\) is 3. \(\boxed{3}\)

Examples

This simple addition of integers is a fundamental skill used in everyday situations, such as managing a bank account. For example, if your balance is \(\$-9\) (an overdraft), you then pay an additional fee of \(\$-12\) (bringing the balance to \(\$-21\)), and finally deposit \(\$24\), your new balance would be \(\$-21 + \$24 = \$3\). Understanding how to handle positive and negative numbers ensures you can track changes in your finances accurately.

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