Practice and Problem-Solving Exercises

A Practice

Graph each inequality. A See Problem 1.

8. y > 2 x + 1 y greater than , 2 x plus 1
9. y < 3 y less than , 3
10. x ≤ 0 x less than or equal to , 0
11. y ≤ x − 5 y less than or equal to , x minus 5
12. 2 x + 3 y ≥ 12 2 x plus 3 y greater than or equal to 12
13. 2 y ≥ 4 x − 6 2 y greater than or equal to 4 x minus 6
14. 3 x − 2 y ≤ 9 3 x minus 2 y less than or equal to 9
15. − y < 2 x + 2 negative y less than 2 x plus 2
16. 5 − y ≥ x 5 minus y greater than or equal to x

17. Cooking The time needed to roast a chicken depends on its weight. Allow at least 20 min/lb for a chicken weighing as much as 6 lb. Allow at least 15 min/lb for a chicken weighing more than 6 lb. See Problem 2.

    1. Write two inequalities to represent the time needed to roast a chicken.
    2. Graph the inequalities.

Graph each absolute value inequality. See Problem 3.

18. y ≥ | 2 x − 1 | y greater than or equal to , vertical line 2 x minus 1 vertical line
19. y ≤ | 3 x | + 1 y less than or equal to , vertical line 3 x vertical line plus 1
20. y ≤ | 4 − x | y less than or equal to , vertical line 4 minus x vertical line
21. y > | − x + 2 | + 1 y greater than , vertical line negative x plus 2 vertical line plus 1
22. y − 7 > | x + 2 | y minus , 7 greater than vertical line x plus 2 vertical line
23. y + 2 ≤ | 1 2 x | y plus 2 less than or equal to absolute value of , 1 half , x , end absolute value ,
24. 3 − y ≥ − | x − 4 | 3 minus y greater than or equal to negative vertical line x minus 4 vertical line
25. 1 − y < | 2 x − 3 | 1 minus y less than vertical line 2 x minus 3 vertical line
26. y + 3 ≤ | 3 x | − 1 y plus 3 less than or equal to vertical line 3 x vertical line negative 1

Write an inequality for each graph. The equation for the boundary line is given. See Problem 4.

27. y = − x − 2 y equals negative x minus 2

    

28. 5 x + 3 y = 9 5 x plus 3 y equals 9

    

29. 2 y = | 2 x + 6 | 2 y equals vertical line 2 x plus 6 vertical line

    

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