First, we need to determine the sum of [tex]\( -117 \)[/tex] and the expression [tex]\( 54 + (-17) \)[/tex].
1. Calculate [tex]\( 54 + (-17) \)[/tex]:
[tex]\[
54 + (-17) = 54 - 17 = 37
\][/tex]
2. Sum the result with [tex]\( -117 \)[/tex]:
[tex]\[
-117 + 37 = -80
\][/tex]
Now, we know the sum of [tex]\( -117 \)[/tex] and [tex]\( 54 + (-17) \)[/tex] is [tex]\( -80 \)[/tex].
Next, we need to understand what should be subtracted from the smallest non-negative integer to get this result of [tex]\( -80 \)[/tex].
3. Identify the smallest non-negative integer:
The smallest non-negative integer is [tex]\( 0 \)[/tex].
4. Set up the equation:
Let [tex]\( x \)[/tex] be the number that we need to subtract. We want:
[tex]\[
0 - x = -80
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
-x = -80
\][/tex]
[tex]\[
x = 80
\][/tex]
Therefore, the number [tex]\( 80 \)[/tex] should be subtracted from the smallest non-negative integer to get the result as the sum of [tex]\( -117 \)[/tex] and [tex]\( 54 + (-17) \)[/tex].
