B Apply

44. Think About a Plan The diagram shows the scores in seconds of a skater's first three trials in a speed-skating event. What is the maximum time she can score on her last trial so that her average time on all four trials is under 36 seconds?

    

    • What do you need to find an average?
    • What inequality can you use to model the situation?

Solve each inequality. Graph the solution.

45. 2 − 3 z ≥ 7 ( 8 − 2 z ) + 12 2 minus 3 z greater than or equal to 7 open 8 minus 2 z close plus 12
46. 6 ( x − 2.5 ) ≥ 8 − 6 ( 3.5 + x ) 6 open x minus 2.5 close greater than or equal to 8 minus 6 open 3.5 plus x close
47. 2 3 ( x − 12 ) ≤ x + 8 2 thirds , open x minus 12 close less than or equal to x plus 8
48. 3 5 ( x − 12 ) > x − 24 3 fifths , open x minus 12 close greater than x minus 24
49. 3 [ 4 x − ( 2 x − 7 ) ] < 2 ( 3 x − 5 ) 3 left bracket 4 x minus open 2 x minus 7 close right bracket less than 2 open 3 x minus 5 close
50. 6 [ 5 y − ( 3 y − 1 ) ] ≥ 4 ( 3 y − 7 ) 6 left bracket 5 y minus open 3 y minus 1 close right bracket greater than or equal to 4 open 3 y minus 7 close
51. Grades Your math test scores are 68, 78, 90, and 91. What is the lowest score you can earn on the next test and still achieve an average of at least 85?
52. Chemistry The pH level of a popular shampoo is between 6.0 and 6.5 inclusive. What compound inequality shows the pH levels of this shampoo? Graph the solution.
53. Geometry The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In Δ A B C , cap delta eh b c comma BC = 4 and A C = 8 − A B . eh c equals 8 minus eh b .  What can you conclude about AB?
54. Writing Write a word problem that can be solved using 25 + 0.5 x ≤ 60 . 25 plus 0.5 x less than or equal to 60 .
55. Error Analysis A classmate solved the inequality 1 2 ( y − 16 ) ≥ y + 2 1 half , open y minus 16 close greater than or equal to y plus 2  as shown. Prove that his answer is incorrect by checking a number that is less than − 20 . negative 20 . (Select a number that makes the computation easy.) What was his error?

    
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56. Construction A contractor estimated that her expenses for a construction project would be between $700,000 and $750,000. She has already spent $496,000. How much more can she spend and remain within her estimate?

Justifying Steps Justify each step by identifying the property used.

57. 3 x ≤ 4 ( x − 1 ) − 8 3 x ≤ 4 x − 4 − 8 3 x ≤ 4 x − 12 − x ≤ − 12 x ≥ 12 table with 5 rows and 2 columns , row1 column 1 , 3 x , column 2 less than or equal to 4 open x minus 1 close minus 8 , row2 column 1 , 3 x , column 2 less than or equal to 4 x minus 4 minus 8 , row3 column 1 , 3 x , column 2 less than or equal to 4 x minus 12 , row4 column 1 , negative x , column 2 less than or equal to negative 12 , row5 column 1 , x , column 2 greater than or equal to 12 , end table
58. 1 2 ( y + 3 ) > 1 3 ( 4 − y ) 3 ( y + 3 ) > 2 ( 4 − y ) 3 y + 9 > 8 − 2 y ) 5 y + 9 > 8 5 y > − 1 y > − 0.2 table with 6 rows and 2 columns , row1 column 1 , 1 half , open y plus 3 close , column 2 greater than , 1 third , open 4 minus y close , row2 column 1 , 3 open y plus 3 close , column 2 greater than 2 open 4 minus y close , row3 column 1 , 3 y plus 9 , column 2 greater than 8 minus 2 y close , row4 column 1 , 5 y plus 9 , column 2 greater than 8 , row5 column 1 , 5 y , column 2 greater than negative 1 , row6 column 1 , y , column 2 greater than negative 0.2 , end table

Solve each compound inequality. Graph the solution.

59. − 6 < 2 x − 4 < 12 negative 6 less than 2 x minus 4 less than 12
60. 4 x ≤ 12  and  − 7 x ≤ 21 4 x less than or equal to 12 , and , minus 7 x less than or equal to 21
61. 15 x > 30  or  18 x < − 36 15 x greater than 30 , or , 18 x less than negative 36

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