For each Compound Inequality listed below, identify 4 solutions and 4 non-solutions, unless the solution set includes all real numbers or there are no solutions.

  • Solutions for intersections (which use and) will make both of the expressions true.

  • Solutions for unions (which use or) will make at least one of the expressions true.

Pay special attention to the numbers in the sample expression! Challenge yourself to use negatives, positives, fractions, decimals, etc.

The first two have been done for you - Answers will vary!

Expression 4 solutions that evaluate to true 4 non-solutions that evaluate to false

a

x > 5 and x < 15

6, 9.5, 12, 14.9

-2, 5, 15, 16.1

b

x > 5 or x < 15

All real numbers

No non-solutions

c

x <= -2 and x > 7

d

x <= -2 or x > 7

e

x < 3.5 and x > -4

f

x < 3.5 or x > -4

g

x >= -1 and x > -5

h

x >= -1 or x > -5

i

x < -4 and x > 2

1 Could there ever be a union with no solutions? Explain your thinking.

2 Could there ever be an intersection whose solution is all real numbers? Explain your thinking.

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