55. Error Analysis John simplified the expression as shown. Describe and correct his error.

    

56. Open-Ended Write an example of an algebraic expression that has a nonnegative value regardless of the value of the variable.

Name the property of real numbers illustrated by the equation.

57. 2 ( s − t ) = 2 s − 2 t 2 open s minus t close equals 2 s minus 2 t
58. − [ − ( x − 10 ) ] = x − 10 negative left bracket negative open x minus 10 close right bracket equals x minus 10
59. − ( 2 t − 11 ) = 11 − 2 t negative open 2 t minus 11 close equals 11 minus 2 t
60. − ( a − b ) = ( − 1 ) ( a − b ) negative open eh minus b close equals open negative 1 close open eh minus b close

C Challenge

61. Simplify 2 ( b − a ) + 5 ( b − a ) 2 open b minus eh close plus 5 open b minus eh close  and justify each step in your simplification.
62. 1. Evaluate the expression 2 ( 2 x 2 − x ) − 3 ( x 2 − x ) + x 2 − x 2 open 2 , x squared , minus x close minus 3 open , x squared , minus x close plus , x squared , minus x  for x = 3. Do not simplify the expression before evaluating it.
    2. Simplify the expression in part (a) and then evaluate your answer for x = 3.
    3. Writing Explain why the values in parts (a) and (b) should be the same.

Standardized Test Prep

SAT/ACT

63. Which expression best represents a simpler form of 4m + 3(m + n)?
    1. 7m + 3n
    2. 4m + 3mn
    3. 3m + 4n
    4. 7 m 2 + 3 n 7 , m squared , plus 3 n
64. A driver drove 12 miles and made a pit stop. After that, the driver continued driving at a constant speed of 65 miles per hour for t hours. Which of the following represents the total distance driven?
    6. 12 + 65t
    7. 65t
    8. 12t + 65
    9. 12(t + 65)
65. What is the value of r when s = − 1 , s equals negative 1 comma  t = 4, and u = 1 5 ? u equals , 1 fifth , question mark

    r = 3 s 2 + 5 ( t − 2 u ) r equals 3 , s squared , plus 5 open t minus 2 u close

    1. 7
    2. 15
    3. 21
    4. 22 1 5 22 , and 1 fifth

Short Response

66. Compare 26 square root of 26  and 4.9. Explain your answer.

Mixed Review

See Lesson 1-2.

Order the numbers from least to greatest.

67. − 1.5 , − 0.5 , − 2 , − 1.4 negative 1.5 comma negative 0.5 comma negative square root of 2 comma negative 1.4
68. − 3 8 , 1 2 , − 3 4 , − 5 6 negative , 3 eighths , comma , 1 half , comma negative , 3 fourths , comma negative , 5 sixths
69. 2 , − 20 , 0.2 , 1 2 square root of 2 comma negative 20 comma 0.2 comma , 1 half
70. 3 4 , − 3 , − 0.5 , − 1 4 3 fourths , comma negative 3 comma negative 0.5 comma negative , 1 fourth

Get Ready! To prepare for Lesson 1-4, do Exercises 71–74.

See Lesson 1-3.

Simplify each expression.

71. 4 x + 3 x − 4 4 x plus 3 x minus 4
72. − p 3 + q 3 − 2 p 3 − q negative , p over 3 , plus , q over 3 , minus , fraction 2 p , over 3 end fraction , minus q
73. − 2 ( 4 + b ) + 4 ( b − 5 ) negative 2 open 4 plus b close plus 4 open b minus 5 close
74. ( k − m ) − ( m − k ) open k minus m close minus open m minus k close

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