Compound Inequalities: Solutions & Non-Solutions

Referenced from lesson Compound Inequalities: Solutions & Non-Solutions (Spring, 2021)

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.

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. 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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