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Question 1103828: Which compound inequality has the set of real numbers 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(13203)   (Show Source):
You can put this solution on YOUR website!
If the solution set to a compound inequality is to be all real numbers, then the compound inequality must use "or"; and the solution sets to the two parts of the compound inequality must overlap. Furthermore, the two parts of the inequality must have one with greater than (or greater than or equal to) and the other with less than (or less than or equal to).
Answer choices a and c use "and", so they can't be the answer.
Answer choice e uses two inequalities that are both "less than", so it can't be the answer.
That leaves b and d as the possible answer. But the two parts of the compound inequality in answer b do not overlap, whereas the two parts in answer d do overlap.
So d is the right answer choice.
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