Answer: The correct option is
(B) −10 + (−90) + (−40)
Step-by-step explanation: We are given to select the expression that is equivalent to the following expression :
[tex]E=-10+(-40)+(-90)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
First, we will evaluate the value of expression (i) as follows :
[tex]E=-10+(-40)+(-90)=-10-40-90=-140.[/tex]
Now, we will evaluate the values of the optional expressions one by one.
Option (A) :
We have
[tex]E_1=10+40+90=50+90=140\neq-140.[/tex]
So, this option is NOT correct.
Option (B) :
We have
[tex]E_2=-10+(-90)+(-40)=-10-90-40=-140.[/tex]
So, this option is CORRECT.
Option (C) :
We have
[tex]E_3=-10-(40-90)=-10-(-50)=-10+50=40\neq-140.[/tex]
So, this option is NOT correct.
Option (D) :
We have
[tex]E_4=-(10-40)+(-90)=-(-30)-90=30-90=-60\neq-140.[/tex]
So, this option is NOT correct.
Thus, the correct option is
(B) −10 + (−90) + (−40)
