Question

PRETTY PLEASE HELP?????? 1. John can spend up to $40 for gasoline and a carwash at a service station. The carwash will cost $6.00 and gasoline costs $4.50 per gallon. The inequality below can be solved for g, the number of gallons of gasoline John can buy.
4.5g + 6 ≤ 40
Which of the following is a true statement? (1 point)
A. John can buy over 10 gallons of gasoline.
B. John can buy at most 7 gallons of gasoline.
C. John can buy 6 gallons but not 7 gallons.
D. John can buy 7 gallons but not 8 gallons.


2. A baseball team had $800 to spend on supplies. The team spent $250 on a new bat. New baseballs cost $3 each. The inequality 250 + 3b ≤ 800 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true? (1 point)
A. The team can purchase 184 new baseballs.
B. The minimum number of new baseballs that can be purchased is 183.
C. The maximum number of new baseballs that can be purchased is 183.
D. The team can purchase 183 new baseballs but this number is neither the maximum nor the minimum.


3. Solve the following inequality. (1 point)
3x + 6 > 15
A. x < 3
B. x > 3
C. x < 7
D. x > 7

4. Solve the following inequality. (1 point)
4x – 6 < 2x + 8
A. x > 1
B. x < 1
C. x > 7
D. x < 7

5. What is the greatest integer that makes the inequality 3 – 2x > 9 a true statement? (1 point)
A. -2
B. 2
C. 5
D. -4

7. Solve the following compound inequality. (1 point)
3x – 3 < -12 OR -4x ≤ -32
A. x ≤ 8
B. -3 < x ≤ 8
C. x < -3
D. x < -3 OR x ≥ 8

8. Solve the following compound inequality. (1 point)
-7x + 9 < 72 AND 5x – 3 ≤ 7
A. x ≤ 2
B. x < -9 AND x ≥ 2
C. -9 < x ≤ 2
D. -10 < x ≤ 2

Answer 1

1. 4.5g + 6 < = 40
    4.5g < = 40 - 6
    4.5g < = 34
    g < = 34/4.5
    g < = 7.56
True statement : John can buy 7 gallons but not 8

2. 250 + 3b < = 800
    3b < = 800 - 250
    3b < = 550
    b < = 550/3
    b < = 183.33
True statement : The maximum number of new baseballs that can be purchased is 183

3. 3x + 6 > 15
    3x > 15 - 6
    3x > 9
     x > 9/3
     x > 3

4. 4x - 6 < 2x + 8
    4x - 2x < 8 + 6
     2x < 14
      x < 14/2
      x < 7

5. 3 - 2x > 9
    -2x > 9 - 3
    -2x > 6 ...when dividing by a negative, u flip the inequality sign
      x < -6/2
      x < -3
     True statement : - 2

7. 3x - 3 < -12         OR     -4x < = -32
    3x < -12 + 3                    x > = -32/-4
    3x < - 9                           x > = 8
      x < -9/3
      x < -3
answer : x < - 3 OR x > = 8

8. -7x + 9 < 72    AND   5x - 3 < = 7
    -7x < 72 - 9                5x < = 7 + 3
    -7x < 63                     5x < = 10
     x > -63/7                     x < = 10/5
     x > - 9                         x < = 2
answer : -9 < x < = 2