SOLUTION: Which compound inequality has the empty set as the solution?
a. x<5 and x≥5
b. x<5 or x>10
c. x<3 and x>-2
d. x≥3 or x<7
e. x<3 or x<-2
Algebra ->
Inequalities
-> SOLUTION: Which compound inequality has the empty set as the solution?
a. x<5 and x≥5
b. x<5 or x>10
c. x<3 and x>-2
d. x≥3 or x<7
e. x<3 or x<-2
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Question 1103829: Which compound inequality has the empty set as the solution?
a. x<5 and x≥5
b. x<5 or x>10
c. x<3 and x>-2
d. x≥3 or x<7
e. x<3 or x<-2 Answer by greenestamps(13200) (Show Source):
The only way to get an empty set with a compound inequality is with an "and". If the compound inequality uses "or", then there will always be solutions.
If a compound inequality using "and" is to have the empty set as the solution, then the solutions to the two parts of the compound inequality must not overlap.
Choices a and c are the only ones that use "and". The two parts for choice c have solution sets that overlap; the two parts for choice a do not (there is no number that is both less than 5 AND greater than or equal to 5).
