Solving Inequalities

1) What is the solution to  
2h+8>3h-6?

• h<14
• h=14
• h>14
• h<2.8

2) A drama club is selling tickets to the spring musical. The auditorium holds 200 people. Tickets cost $12 at the door, x, and $8.50 if purchased in advance, y. The drama club has a goal of selling at least $1000 worth of tickets to Saturday’s show. Write a system of inequalities that can be used to model this scenario.

• x+y ≥ 200
  12x+8.50y< 1000
• x+y≤200
  12x+8.50y≥1000
• x+y ≥ 1000
  12x+8.50y≤200
• x+y ≥ 1000
  12x+8.50y< 2000

3) If 50 tickets are sold in advance, what is the minimum number of tickets that must be sold at the door so that the club meets its goal? 

• 150
• 149
• 49
• 48

4) The acidity in a swimming pool is considered normal if the average of three pH readings, p, is defined such that  If the first two readings are 7.2 and 7.6, which value for the third reading will result in an overall rating of normal?

• 6.2
• 8.6
• 7.3
• 8.8

5) When 3x+2 ≤ 5(x-4) is solved for x, the solution is

• x ≤ 3
• x ≥ 3
• x ≤ -1
• x ≥ 11

6) Which inequality is represented by this graph?

• y ≤ 2x-3
• y ≤ 3x+2
• y  ≥ 2x-3
• y ≥ 3x+2

7) The sum of two numbers, x and y, is more than 8. When you double x and add it to y, the sum is less than 14. Write a system of inequalities that can be used to model this scenario.

• x+y>8
  2x+y≤14
• x+y≥8
  x+2y≤14
• x(y)<8
  2x+y<14
• x+y>8
  2x+y<14

8) Which point is included in the solution set of question 7?

• (6,2)
• (8,-1)
• (1,9)
• (10,0)

9)  The cost of a pack of chewing gum in a vending machine is $0.75. The cost of a bottle of juice in the same machine is $1.25. Julia has $22.00 to spend on chewing gum and bottles of juice for her team and she must buy seven packs of chewing gum. If b represents the number of bottles of juice, which inequality represents the maximum number of bottles she can buy? 

• 0.75b+1.25(7)≥22
• 0.75(7)+1.25b ≥ 22
• 0.75b+1.25(7) ≤  22
• 0.75(7)+1.25b ≤ 22

10) Which graph represents the solution of y≤x+3 and y≥-2x-2

• Graph 1
• Graph 3
• Graph 2
• Graph 4