Greatest value for -1 < x < 0
We are going to analyze each answer
A. x
In this answer -1 < x < 0, then its greatest value is 0
B. 2x
Since -1 < x < 0. In this answer:
-1 · 2 < x · 2 < 0 ·2 [multiplying each term by 2]
-2 < 2x < 0
then the greatest value of 2x is 0
C. x + 1
Since -1 < x < 0. In this answer:
-1 + 1 < x + 1 < 0 + 1 [adding 1 on each term]
0 < x + 1 < 1
then the greatest value of x + 1 is 1
D. 1/x
Since -1 < x < 0 then -1 < x and x < 0. In this answer:
-1 / x > x / x and x / x > 0 / x [We divide by x each term]
- 1 / x > 1 and 1 > 0
1 / x < - 1 [multiplying by -1]
then the greatest value of 1 / x is -1
E. -1/x
On the last answer (D) we found in the second step that - 1 / x > 1
Then the greatest value of -1/x is infinite
Answer: E