Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
3a. 1, 2, 3, or 4 cases b. ^ = 16|, but you cannot
walk | of a dog. If you round down to 16, you will only
make $72. So round up to 17.


  1. x < 2 *■ i i ©— i--------- 1 - 1 —
    0 1 2 3 4 5
    Lesso n Ch eck 1. D 2. B 3. A 4. C 5a. Multiplication
    by -2 ; it is the inverse of division by -2. b. Addition of
    4; it is the inverse of subtraction of 4. c. Division by - 6 ;
    it is the inverse of multiplication by -6. 6. The inequality
    symbol was not reversed when multiplying by a negative.
    —5 ( —f) < -5(2), n < —10
    Ex er ci ses

  2. x> -10

  3. p < 32 -


-12 -1 0 - 8 - 6 - 4 - 2
I I 0 I— I— I— I-

(^28 3032 3436)



  1. v< -3 i-
    -5 -4 -3 -2 -1

  2. x> -3

  3. m<0 -


-5 -4 -3 -2 -1
-I— I— I-
2 - 1


  1. m<2

  2. m>2


21.c>6
8 10


  1. z> -3
    -5 -4 -3 -2 -1

  2. b :
    1 1

  3. h> -13
    -15 -14 -13 -12 -11 -10

  4. q < 9
    6 7 8 9 10

  5. no more than 66 text messages 33-35. Answers
    may vary. Samples are given. 33. -5, -4, -3, -2

  6. -6, -5, -4, -3 37. Multiply each side by - 4 and
    reverse the inequality symbol. 39. Divide each side by 5.

  7. -2 43. 4 45. Sometimes true; sample: It is true
    when x = 4 and y = 0.5 but false when x = 4 and
    y = -2. 47. Sometimes true; sample: It is true when
    x = 4 and y = 2 but false when x = 0 and y = 2.

  8. at least 0.08 mi per min

  9. 3(-1)>3(§)
    -3 >t

  10. 2(0.5) < 2 (lc )


1 < c


  1. 5(f) <5(—2)
    n< -10


Mult. Prop, of Ineq.
Simplify.
Mult. Prop, of Ineq.
Simplify.
Mult. Prop, of Ineq.
Simplify.


  1. -^(1) > (_ f s) Mult. Prop, of Ineq.
    — 5 > s Simplify.

  2. If the most expensive sandwiches and drinks are
    ordered, the cost is 3(7) + 3(2) = 27, leaving $3. If the
    most expensive snack is bought, the least number of
    snacks you can afford is 1. If the least expensive
    sandwiches and drinks are ordered, the cost is
    3(4) + 3(1) = 15, leaving $15. If the least expensive snack
    is bought, the greatest number of snacks you can afford is



    1. x < 20, x < 30, x < 40,... ; any inequality
      following the one that a is a solution to. This is because
      each following inequality has the same solutions as the
      previous inequalities, with more values as solutions.



  3. 3.14d> 29.5 and d > 9.4, so the men's basketballs
    need a 10-in. box; 3.14d> 27.75, d> 8.8 so the youth
    basketballs need a 9-in. box. 65. D 67. w = € — 3,
    18 = 2€ + 2(€ - 3), 18 = 4€ - 6 , 24 = 4€, so € = 6
    (Length is 6 in.). 68. x<-11 69. y > 13.6 70. g<5

  4. —| > c 72. - 1 < b 73. y<75 74.2 75. -2

  5. 1
    Lesso n 3-4 pp. 186-192
    Go t I t? 1a. 3 2 - 4 b. n < 3 c. x < 25 2. any width
    greater than 0 ft and less than or equal to 6 ft 3. m < -3
    4a. b > 3 b. Answers may vary. Sample: adding 1 to
    each side. This would gather the constant terms onto one
    side of the inequality. 5a. no solution b. all real numbers
    Lesso n Ch eck 1. a > 2 2. f < 5 3. z< 13 4. no
    solution 5. greater than 0 cm and less than or equal to
    8 cm 6. The variable terms cancel each other out and a
    false inequality results. 7. Yes; each side can be divided by
    2 first. 8. No; there is no solution, since -6 is not greater
    than itself. If the inequality symbol were >, your friend
    would be correct.
    Ex e r c i se s 9. f< 3 11.y> -2 13. r>3.5

  6. 5s> 250;s> 50 mph 17. k> 1 19. y < - 1

  7. z<9 23. x< 3 25. f< 6 27. m> -5 29. all
    real numbers 31. all real numbers 33. all real numbers

  8. x> -4 37. f> | 39. n > -2 41. a >0 .5

  9. k:^13 45. 5.5 h 47. D 49a. v> 4 b. 4 < v
    c. They are equivalent, d. Check students' work. 51. at
    least $3750 53. 3y was subtracted from instead of added
    to each side; 7y< 2, y <y. 55. -5, -4, -3, -2, -1,0,
    1, 2, 3, 4, 5, and 6 57a. 73 boxes b. 4 trips
    Lesson 3-5 pp. 194-199
    Go t It? 1. N= {2, 4, 6, 8, 10, 12}; N= {x|x is
    an even natural number, x < 12} 2. {n|n < -3 }
    3a. {} or 0, {a}, {b}, {a, b}; { } or 0, {a}, {b}, {c},
    {a, b}, {a, c}, {b, c}, {a, b, c} b. Yes; every element
    of set A is part of set B, since -3 < 0. 4. A' = {February,
    April, June, September, November}


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