Referenced from lesson Compound Inequalities: Solutions & Non-Solutions

For each Compound Inequality listed below, identify 4 solutions and 4 non-solutions. If there are no solutions or the solution set includes all real numbers you can write that instead of making a list.

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

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

x > 5 and x < 15

6, 9.5, 12, 14.9

-2, 5, 15, 16.1

x > 5 or x < 15

All real numbers

No non-solutions

x <= -2 and x > 7

x <= -2 or x > 7

x < 3.5 and x > -4

x < 3.5 or x > -4

x >= -1 and x > -5

x >= -1 or x > -5

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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