Let’s break down the expression step-by-step:
1. Initial Expression:
[tex]\[
-53 + (23 + 26)
\][/tex]
2. Step 1: Compute [tex]\(23 + 26\)[/tex]:
[tex]\[
23 + 26 = 49
\][/tex]
3. Result:
[tex]\[-53 + 49\][/tex]
4. Evaluate the expression:
[tex]\[
-53 + 49 = -4
\][/tex]
We can also rewrite the expression by re-pairing the numbers using the associative property of addition. Observe the following equivalent steps:
- First Re-pairing:
- Group [tex]\(-53\)[/tex] and [tex]\(23\)[/tex]:
[tex]\[
(-53 + 23) + (26)
\][/tex]
- Compute [tex]\(-53 + 23\)[/tex]:
[tex]\[
-53 + 23 = -30
\][/tex]
- Result:
[tex]\[
-30 + 26
\][/tex]
- Evaluate the expression:
[tex]\[
-30 + 26 = -4
\][/tex]
- Second Re-pairing (identical to the initial step but just verifying for consistency):
- Group [tex]\(23\)[/tex] and [tex]\(-53\)[/tex]:
[tex]\[
(23 - 53) + (26)
\][/tex]
- Compute [tex]\(23 - 53\)[/tex]:
[tex]\[
23 - 53 = -30
\][/tex]
- Result:
[tex]\[
-30 + 26
\][/tex]
- Evaluate the expression:
[tex]\[
-30 + 26 = -4
\][/tex]
- Third Re-pairing:
- Group [tex]\(23 + 26\)[/tex] first:
[tex]\[
(23 + 26) + (-53)
\][/tex]
- Computing [tex]\(23 + 26\)[/tex] again for completeness:
[tex]\[
23 + 26 = 49
\][/tex]
- Result:
[tex]\[
49 + (-53)
\][/tex]
- Evaluate the expression:
[tex]\[
49 - 53 = -4
\][/tex]
Combining all these steps, we see that regardless of how we group the numbers, the outcome is the same:
[tex]\[
-53 + (23 + 26) = (-53 + 23) + 26 = (23 - 53) + 26 = (23 + 26) + (-53) = -4
\][/tex]
Thus, the final result of the given expression is:
[tex]\[
-4
\][/tex]
