1. Look at Part 1. What number is the circle on?

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   1

2. What type of inequalities have solution sets with closed circles?

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   Greater than or equal to (\ge) and Less than or equal to (\le).
   

3. Are the values in the solution set greater than 1​ or less than 1? How do you know?

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   Greater than 1. Possible explanation: The red line and arrow are pointing toward values greater than 1 (2, 3, 4, ...).
   

4. Which inequality could you use to represent this solution set?

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   D, x\ge 1

5. Look at Part 2. What steps can you use to solve this inequality?

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   Add 3 to both sides of the inequality, then divide both sides of the inequality by -2​.
   

6. Will either step change the direction of the inequality symbol? How do you know?  

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   Yes; dividing both sides of the inequality by -2​ will change the inequality symbol. Multiplying or dividing both sides of an inequality by a negative number changes the direction of the symbol.
   

7. What is the solution to the inequality?

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   x\lt-4

8. Look at Part 3. What property was used to get the equation in Step 1?

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   The distributive property.

9. What other step(s) could you have taken to start solving this equation?

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   Possible answers: Subtract 4x from both sides of the equation; Subtract 2x from both sides of the equation.
   

10. What is the justification for Step 2?

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    Combining like terms. 

11. What property allows Step 3?

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    The subtraction property of equality.
    

12. What operations were performed in Steps 4 and 5?

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    Adding 3 to both sides of the equation and dividing both sides of the equation by 5​. 

13. How can you check to confirm that x=3​ is a solution to the original equation?

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    Substitute x=3​ back into the original equation and verify that it makes the equation true.

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