37. Solve | y | ≥ x . vertical line y vertical line greater than or equal to x .  (Hint: Write two inequalities and then graph them.)
38. Student Art A teacher wants to post a row of student artwork on a wall that is 20 ft long. Some pieces are 8.5 in. wide. Other pieces are 11 in. wide. She is going to leave 3 in. of space to the left of each art piece. She wants to post at least 16 pieces of art. Write and graph a system of inequalities that describes how many pieces of each size she can post.

Standardized Test Prep

SAT/ACT

39. The point ( − 3 , 11 ) open negative 3 comma 11 close  is a solution of which of the following systems?

    1. y ≥ x − 2 y greater than or equal to x minus 2

       2 x + y ≤ 5 2 x plus y less than or equal to 5

    2. y > x + 8 y greater than x plus 8

       3 x + y > 2 3 x plus y greater than 2

    3. y > − x + 8 y greater than negative x plus 8

       2 x + 3 y ≥ 7 2 x plus 3 . y greater than or equal to 7

    4. y ≤ − 3 x + 1 y less than or equal to , minus 3 , x plus 1

       x − y ≥ − 15 x minus y greater than or equal to , minus 15

40. A plane has 18 passengers. Some have 1 bag and others have 2 bags. There are a total of 27 bags. Let b = b equals  the number of passengers with 1 bag and t = t equals  the number of passengers with 2 bags. Which system describes this situation?

    6. b + t = 27 b plus t equals 27

       b + 2 t = 18 b plus 2 t equals 18

    7. t = 18 − b t equals 18 minus b

       b + 2 t = 27 b plus 2 t equals 27

    8. b + t = 18 b plus t equals 18

       b = 27 + 2 t b equals 27 plus 2 t

    9. b = 18 − t b equals 18 minus t

       b + 2 t = 18 b plus 2 t equals 18

41. You fill your glass with ice and then add room-temperature water. Which graph best represents the change in temperature of the glass?

    1. 
    2. 
    3. 
    4. 

Extended Response

42. Suppose the line through points ( − 1 , 6 ) open negative 1 comma 6 close  and (x, 2) is perpendicular to the graph of 2 x + y = 3 . 2 x plus y equals 3 .

    1. Find the value of x. Show your work.
    2. What is an equation of the line perpendicular to the graph of 2 x + y = 3 2 x plus y equals 3  and through the given points?
    3. What ordered pair is a solution of both equations? Explain.

Mixed Review

See Lesson 6-5.

Graph each linear inequality.

43. y − x ≤ 3 y minus x less than or equal to 3
44. 3 y + x > 4 3 y plus x greater than 4
45. y ≤ 5 y less than or equal to 5

Get Ready! To prepare for Lesson 7-1, do Exercises 46–48.

See Lesson 1-2.

Simplify each expression.

46. ( 1 + 3 ) 2 − ( 1 + 3 ) open 1 plus 3 close squared . minus open 1 plus 3 close
47. 4 3 + 5 2 + ( 4 − 3 ) 1 4 cubed , plus , 5 squared , plus . open 4 minus 3 close to the first
48. 7 2 + 2 ( 3 3 + 5 ) 7 squared , plus 2 open , 3 cubed , plus 5 close

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