Name: __________________ Class: ________
Inequality Practice Booklet
1. Graph the following inequalities. Pay attention to whether the boundary point is open or closed. List
three possible solutions.
Inequality
a) x  3
Graph
Solutions
b) x  0.75
c) x  
4
5
d) x  6
e)  3  x  5
f)
9 x3
2. For the following graphs write the inequality and list three possible solutions.
Inequality
a)
b)
c)
Graph
Solutions
Name: __________________ Class: ________
d)
e)
3. Determine the values that are solutions to the following inequalities by circling the correct solutions.
Inequality/Limit
Possible Solutions
x  0.8
x  16.5
2,0.8,0.9,0.5,0.8,1.2
16.5,16.4,16.05,16.62,16.49
2
 x
5
1 3 1 2 3 5
 , , , , ,
5 5 2 5 4 8
5
x2
6
5
16 7
2.8, ,2.92, ,2 ,2.6
2
6 8
4. Solve and verify the following inequalities.
Solve
8.6  x  5.2
3.1 y  12.4
Verify
Verify
Verify
Name: __________________ Class: ________
x
 30
5
2
x
1 .2
5x  19  36
7 x  2x  30
Rule for Multiplying and Dividing by a Negative:
Name: __________________ Class: ________
5. Solve and verify the following inequalities.
Solve
 2 y  24
x
 9
4
1
x5
6
 2x  4  20
 5 y  91  36
Verify
Verify
Verify
Name: __________________ Class: ________
10x  22  8x
Solve
5x  8  4x  12
9 y  17  8  6.5 y
Verify
Verify
 3x  5  3x  9
 2( x  3)  10 x  18

2
3 1
x 
3
4 4
Name: __________________ Class: ________
Name: __________________ Class: ________
6. The manager of a clothing store has set goals for her sales staff. Express each inequality algebraically.
a) The monthly sales m, will be a minimum of $18 000.
b) At month end, the total time t, spent counting inventory would
be at most 8 hours.
c) The value of total sales will be more than $7000.
Represent each situation using an inequality. Solve the inequality verify your solution. Include units.
7. The student council decides to raise money by organizing a dance. The cost of hiring a DJ is $1200 and the
students’ council is charging $7.50 per ticket. How many tickets can be sold to make a profit more than
$1500?
8. Yvonne is planting trees as a summer job. She gets paid $0.10 per tree planted. She wants to earn at least
$20 per hour. How many trees must she plant per hour in order to achieve her goal?
9. The Super Fencing Company builds cedar fences at a cost of $85 per section of fence. How many sections
of Fence could they afford to buy if they could spend no more than $1400?
10. The cost of a prom is $400 to rent a hall, and $30 per person for the meal. The prom committee has
$10,000. How many students can attend?
Name: __________________ Class: ________
11. Molly has a candle making business. Her costs are $200 plus $0.75 per candle made. She charges her
customers $3.50 per candle. If she sells all of the candles she makes, how many candles sold will allow her
to make a profit?
12. Jake plans to board his dog at a Kennel while he is away at the NCAA Final Four Basketball tournament.


Kennel A: $90 plus $5 a day
Kennel B: $100 plus $4 a day
For how many days must Jake board his dog so that Kennel A will be less expensive than Kennel B?
13. Sarah has two offers for positions as a sales position at two local stores. What do Sarah’s sales need to be
for Store B to be a better offer?
 Store A will pay a flat rate of $55 per day plus 3% of sales
 Store B will pay a flat rate of $40 per day plus 5% of sales
14. Patricia wants to buy a new pair of ice skates that cost $250. She already has $86 dollars that she plans on
using towards this purchase. She earns $10.25 per hour at her part time job. What is the minimum number
of hours that she must work to save enough money to purchase the pair of ice skates.
Name: __________________ Class: ________
15. The two diagrams shown below that both represent the inequality x  3 are numbered
a. I and III
b. I and IV
c. II and III
d. II and IV
16. What integers could represent the value of x in the inequality statement:
1 3
  0.5
4 x