Inequalities Review Sheet
Name:
Date:
Block:
> 22
3. 8x – 9 < -2x + 31
Solve each inequality. (SOL A.5a)
1.
<7
2.
b > -21
x > 55
x<4
4. 3(2x – 7) > 4(x - 6) -5
5. 3(x + 3) + 1 > 3x + 7
6. 7 - x > 2
x > -4
All real #s
x≤5
Solve each compound inequality. (SOL A.5a)
Hint: There are TWO SPECIAL CASES. Can you find them?
7. 4 – x < 2 or 5 ≥ x – 7
8. -12 < 6(x – 2) < 18
x > 2 or x ≤ 12 becomes
All Real #s
0≤x<5
9. -5x + 13 > 33 or 4(x + 4) < 28
10. -3 < 10x + 17 < 57
x < -4 or x ≤ 3 becomes
x≤3
-2 ≤ x ≤ 4
Graph each inequality. (SOL A.5a)
See Mrs. Neterer to check.
11. -4 < x < 0
12. x < 5 or x > 8
13. -4 < x or x ≤ 0
14. -7 ≤ x ≤ -2
Word Problems Review Sheet
Directions: Write an equation, proportion, or inequality to represent each word problem below.
Solve. Show all of your work and circle your final answers. When it is appropriate, round
decimals to the nearest hundredth.
1. Tara is four less than three times Josh’s age. Together, their ages equal 44. Find both of
their ages.
3J – 4 + J = 44
Josh is 12 years old and Tara is 32 years old.
2. Ms. Frizzle buys seven pencils for every three students on the Magic School Bus. She is
expecting 30 students on her bus next weekend. How many pencils should she buy?
70 pencils
3. Jared makes HUGE batches of cookies that feed hundreds of people! When he is making
the cookie dough he puts in seven cups of flour for every three cups of sugar. If Jared has to
put ten cups of sugar in the recipe, how many cups of flour will he need?
23 1/3 cups
4. A new plasma-screen television costs $3033. A family makes a down payment of $630 and
pays off the balance in 12 equal monthly payments. Find the monthly payment.
630 + 12m = 3033
$200.25
5. On Monday, biologists tagged 200 sunfish from a lake. On Friday, the biologists counted 19
tagged fish out of a sample of 400 sunfish from the same lake. Estimate the total number of
sunfish in the lake.
222 fish
6. To become a member of an ice skating rink, you have to pay a $65 membership fee. The
cost of admission to the rink is $6 for members and $12 for nonmembers. After how many
visits to the rink is it less expensive to be a member than a nonmember?
65 + 6m < 12m
11 visits or more
7. Jessica is three more than five times Mark’s age. Together, their ages equal 81. Find both
of their ages.
5m + 3 + m = 81
Mark is 13 years old and Jessica is 68 years old.
8. A gas station charges $0.20 less per gallon of gasoline if a customer also gets a car wash.
The price of gas is regularly $3.75 a gallon and a car wash is $10.00. If you get a car wash,
what are the possible amounts of gasoline (in gallons) that you can buy if you can spend at
most $40?
3.55g + 10 ≤ 40
8.45 gallons or less
9. A man who is 5.8 feet tall stands next to the Washington Monument. The sun’s rays strike
the man and cast a shadow that is 2.5 feet. If the Washington Monument is 555 feet tall,
estimate the length of its shadow.
239.22 feet
10. Your cell phone plan costs $79.99 per month for a given number of minutes. Each
additional minute or part of a minute costs $0.35. You budgeted $100 per month for phone
costs. Write and solve an inequality to determine the possible number of additional minutes
(m) that you can afford each month.
79.99 + .35m ≤ 100
57 minutes or less
11. Shirlie wants to buy a new Chevy Cruze for $20,875. She makes a down payment of $5,275
and pays off the balance in 48 equal monthly payments?
5,275 + 48m = 20,875
$325
12. You need to have at least $400 in your checking account to avoid a low balance fee. You
have $852 in your account now and you make withdrawals of $40 per week. Determine the
possible number of weeks that you can withdraw money and avoid paying the fee.
852 – 40w ≥ 400
11 weeks or less
13. Camp Far From Home allows campers to take the horses out for joy rides through the woods
for an additional fee. The camp typically charges campers $20 per ride. However, there are
some campers who like to ride so often, the camp recommends they join the riding club.
The membership fee is $75, but members are only charged $10 per ride. What are the
possible number of rides a camper could take that would make it less expensive to join the
riding club?
75 + 10r < 20r
8 rides or more
Properties Review Sheet
Directions: Using the axioms of inequality and the properties of real numbers,
justify each step in the solutions given below.
Solution
3(x + 4) > 60
Justification
Given
3x + 12 > 60
Distributive Property
3x + 12 - 12 > 60 - 12
Subtraction Property of Inequality
3x + 0 > 48
Inverse Property of Addition
3x > 48
Identity Property of Addition
(3x) >( )(48)
Multiplication Property of Inequality
1x > 16
Inverse property of Multiplication
x > 16
Identity Property of Multiplication
Solution
w∙3 - 5 > 85
Justification
Given
3w – 5 > 85
Commutative Property of Multiplication
3w – 5 + 5 > 85 + 5
Subtraction Property of Inequality
3w + 0 > 90
Inverse Property of Addition
3w > 90
Identity Property of Addition
(3w) >( )(90)
Multiplication Property of Inequality
1w > 30
Inverse property of Multiplication
w > 30
Identity Property of Multiplication