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, 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`

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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