To determine which expression is equivalent to [tex]\(-10 + (-40) + (-90)\)[/tex], we will analyze each of the given expressions step-by-step and compare their results.
1. Expression 1: [tex]\(-10 + (-40) + (-90)\)[/tex]
[tex]\[
-10 + (-40) + (-90) = -10 - 40 - 90 = -140
\][/tex]
2. Expression 2: [tex]\(-10 + (-90) + (-40)\)[/tex]
[tex]\[
-10 + (-90) + (-40) = -10 - 90 - 40 = -140
\][/tex]
This expression simplifies to [tex]\(-140\)[/tex], which is the same as Expression 1.
3. Expression 3: [tex]\(10 + 40 + 90\)[/tex]
[tex]\[
10 + 40 + 90 = 140
\][/tex]
This expression simplifies to [tex]\(140\)[/tex], which is not the same as Expression 1.
4. Expression 4: [tex]\(-(10 - 40) + (-90)\)[/tex]
[tex]\[
10 - 40 = -30 \\
\text{Thus, } -(10 - 40) = -(-30) = 30 \\
\text{So, } 30 + (-90) = 30 - 90 = -60
\][/tex]
This expression simplifies to [tex]\(-60\)[/tex], which is not the same as Expression 1.
5. Expression 5: [tex]\(-10 - (40 - 90)\)[/tex]
[tex]\[
40 - 90 = -50 \\
\text{Thus, } -10 - (40 - 90) = -10 - (-50) = -10 + 50 = 40
\][/tex]
This expression simplifies to [tex]\(40\)[/tex], which is not the same as Expression 1.
From the comparisons, we see that only Expression 2: [tex]\(-10 + (-90) + (-40)\)[/tex] simplifies to [tex]\(-140\)[/tex], which is equivalent to [tex]\(-10 + (-40) + (-90)\)[/tex].
Therefore, the equivalent expression is:
[tex]\[
-10 + (-90) + (-40)
\][/tex]
