100 points to right
a compound inequality is graphed, and its graph consists of all real numbers. which open sentence could have resulted in this solution set?

a)r > 5 or r > –1

b)r > 5 or r < –1

c)r < 5 or r < –1

d)r < 5 or r > –1

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The answer is option D)  r < 5  or  r > – 1.

I'm going to graph each inequality below on a number line.

A)  r > 5  or  r > – 1.



The result is found just by joining those two intervals together. Actually that compound inequality only implies

r > – 1

which does not represent all real numbers.

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B)  r > 5  or  r < – 1.



Numbers between – 1  and  5 (including them) are not included in the union, so you don't have all real numbers represented there either.

—————

C)  r < 5  or  r < – 1.



Numbers that are greater or equal to 5 are not in the union. So it does not represent all real numbers.

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D)  r < 5  or  r > – 1.



Now all real numbers are included in the union. So this is the right choice.

  option D)  r < 5  or  r > – 1.

I hope this helps. =)