To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Solving Inequalities (using Multiplication and Division) Worksheet

Solving Inequalities (using Multiplication and Division) Worksheet
  • Page 1
 1.  
Which numbers are the solutions of the inequality, x + 5 < 3?
a.
2
b.
- 1
c.
- 5


Solution:

The total number of lawns mowed by {Hename[1]} in a week = the number of lawns mowed from Monday to Saturday + the number of lawns mowed on Sunday.

The number of lawns mowed from Monday to Saturday = the number of days from Monday to Saturday x the number of lawns mowed on each day = 6 × 1 = 6.

The total number of lawns mowed by {Hename[1]} in a week = 6 + 2 = 8.
[Number of lawns mowed on Sunday = 2.]

The total number of lawns mowed in 3 weeks = 3 × the number of lawns mowed in a week.

= 3 × 8
[Substitute the values.]

The total number of lawns mowed by {Hename[1]} in three weeks is 24.


Correct answer : (4)
 2.  
Which numbers are the solutions of the inequality, x - 7 > 2?
a.
9
b.
5
c.
12
d.
- 5


Solution:

Total number of {Q18215B[1]}s owned = {val1} + Number by which they are increased

= {val1} + z

The expression that describes the number of {Q18215B[1]}s owned by {Hename[1]} is {val1} + z.


Correct answer : (3)
 3.  
Which numbers are the solutions of the inequality, x + 5 < 3?
a.
- 5
b.
- 1
c.
2


Solution:

The total number of lawns mowed by {Hename[1]} in a week = the number of lawns mowed from Monday to Saturday + the number of lawns mowed on Sunday.

The number of lawns mowed from Monday to Saturday = the number of days from Monday to Saturday x the number of lawns mowed on each day = 6 × 1 = 6.

The total number of lawns mowed by {Hename[1]} in a week = 6 + 2 = 8.
[Number of lawns mowed on Sunday = 2.]

The total number of lawns mowed in 3 weeks = 3 × the number of lawns mowed in a week.

= 3 × 8
[Substitute the values.]

The total number of lawns mowed by {Hename[1]} in three weeks is 24.


Correct answer : (1)
 4.  
Which of the choices represents the solution for the inequality, 9x > 81?
a.
x > 9
b.
x ≤ 9
c.
x < 9
d.
x ≥ 9


Solution:

9x > 81
[Original inequality.]

9x9 > 81 / 9
[Divide by 9 on both sides, according to division property, if c > 0 and a > b then ac > bc.]

x > 9
[Simplify.]


Correct answer : (1)
 5.  
Which of the choices represents the solution for the inequality, 3x > 9?
a.
x ≤ 3
b.
x > 3
c.
x ≥ 3
d.
x < 3


Solution:

3x > 9
[Original inequality.]

3x3 > 9 / 3
[Divide by 3 on both sides, according to division property, if c > 0 and a > b then ac > bc.]

x > 3
[Simplify.]


Correct answer : (2)
 6.  
The cost of one xerox copy is 5 cents per page. Francis cannot spend more than 150 cents on xerox. Express the number of pages he can get xeroxed as an inequality.
a.
x > 30
b.
x < 30
c.
x ≤ 30
d.
x ≥ 30


Solution:

Let x be the number of pages he can get xeroxed.

5x ≤ 150
[Original inequality.]

5x51505
[Divide each side by 5.]

x ≤ 30
[Simplify.]


Correct answer : (3)
 7.  
Solve the inequality - 10a ≤ 50.
a.
a > 5
b.
a < 5
c.
a ≥ - 5
d.
a ≤ - 5


Solution:

- 10a ≤ 50
[Original equation.]

- 10a- 1050- 10
[Divide each side by - 10 and reverse the direction of the inequality.]

a ≥ - 5
[Simplify.]


Correct answer : (3)
 8.  
Solve the inequality -6b > 48.
a.
b < -8
b.
b < 8
c.
b > -8
d.
b > 8


Solution:

-6b > 48
[Original inequality.]

-6b-6 < 48-6
[Divide each side by -6 and reverse the inequality symbol.]

b < -8
[Simplify.]


Correct answer : (1)
 9.  
Solve the inequality - 7k ≥ 56.
a.
k ≥ - 8
b.
k ≤ - 8
c.
k ≥ 8
d.
k ≤ 8


Solution:

- 7k ≥ 56
[Original inequality.]

- 7k- 756- 7
[Divide each side by - 7 and reverse the inequality symbol.]

k ≤ - 8
[Simplify.]


Correct answer : (2)
 10.  
Rebecca has $150, with which she can buy at most 3 dresses. Find the maximum cost of each dress she can buy.
a.
$49
b.
$51
c.
$50
d.
None of the above


Solution:

Let x be the cost of each dress.

As she can buy at most 3 dresses, the total cost of the 3 dresses is less than or equal to $150.

3x ≤ 150
[Write the inequality.]

3x31503
[Divide by 3 on each side.]

x ≤ 50
[Simplify.]

The maximum cost of each dress is $50.
[As x ≤ 50, the maximum value of x is 50.]


Correct answer : (3)

*AP and SAT are registered trademarks of the College Board.