1. Look at Part 1. What is a compound inequality? 

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   A set of two or more inequalities connected by AND or OR.
   

2. What inequality can you write to describe the smallest value of x​ included in the solution set shown? Justify your response.

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   x\ge-6; the circle is closed at -6, which means that the solution includes -6 and all values greater than -6​ that are shaded.
   

3. What other inequality can you write for the solution set shown?

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   x\lt5

4. What are two ways you can write the compound inequality represented in Part 1?

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   x\ge-6 AND x\lt5; -6\le x\lt5

5. Look at Part 2. What is the equation of the red line?

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   y=x+5

6. What is the equation of the blue line?

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   y=-3x+1

7. Is (0,5) a solution to the equation y=x+5​? Justify your answer algebraically and graphically.

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   Yes; (0,5) makes a true equation when it is substituted into y=x+5, and it falls on the line.
   

8. Give an example of a point that is not a solution to​ y=-3x+1.​ Why isn't it a solution?

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   Answers vary. Students should choose any point that is not on the line of y=-3x+1; they can show that (1) it does not make the equation true and (2) it does not fall on the line. 

9. How is the solution to a system of equations represented on a graph?

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   It is the point where the graphs of the two equations intersect.
   

10. What is the solution to this system?

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    (-1,4)

11. How can you verify that this ordered pair is correct?

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    Substitute its values into the two equations you came up with; it should make both equations true.

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