PROPERTIES OF INEQUALITIES WORKSHEET

Problems 1-10 : Solve each inequality. 

Problem 1 : 

Solve the following inequality and graph the solution. 

x + 7 < 13

Problem 2 : 

Solve the following inequality and graph the solution. 

y - 4 > -7

Problem 3 : 

Solve the following inequality and graph the solution. 

0.9 ≥ a - 0.2

Problem 4 : 

Solve the following inequality and graph the solution. 

b + 6.2 ≥ 9.2

Problem 5 :

4k > 24

Problem 6 :

y/2 > -1.5

Problem 7 :

2m/3 ≤ 6

Problem 8 :

-b/10 ≥ -0.11

Problem 9 :

10 ≥ -x

Problem 10 :

-0.25h > 4.25

Problem 11 :

The memory in William’s camera phone allows her to take up to 25 pictures. William has already taken 21 pictures. Write, solve, and graph an inequality to show how many more pictures William could take. Check your answer.

Problem 12 :

David can bench press 225 pounds. He wants to bench press at least 260 pounds. Write and solve an inequality to determine how many more pounds David must lift to reach his goal. Check your answer.

Problem 13 :

James has a $16 gift card for a health store where a smoothie costs $2.50 with tax. What are the possible numbers of smoothies that James can buy?

Problem 14 :

A pitcher holds 78 ounces of juice. What are the possible numbers of 10-ounce servings that one pitcher can fill?

Detailed Answer Key

1. Answer : 

x + 7 < 13

Because 7 is added to x, subtract 7 from each side to undo the addition.

(x + 7) - 7 < (13) - 7

x + 7 - 7 < 13 - 7

x < 6

2. Answer : 

y - 4 > -7

Because 4 is subtracted from y, add 4 to each side to undo the subtraction.

(y - 4) + 4 > (-7) + 4

y - 4 + 4 > -3

y > -3

3. Answer : 

0.9 ≥ a - 0.2

Because 0.2 is subtracted from a, add 0.2 to each side to undo the subtraction.

(0.9) + 0.2 ≥ (a - 0.2) + 0.2

0.9 + 0.2 ≥ a - 0.2 + 0.2

0.11 ≥ a

a ≤ 0.11

4. Answer : 

b + 6.2 ≥ 9.2

Because 6.2 is added to b, subtract 6.2 from each side to undo the subtraction.

(b + 6.2) - 6.2 ≥ (9.2) - 6.2

b + 6.2 - 6.2 ≥ 9.2 - 6.2

b ≥ 3

5. Answer : 

4k > 24

Because k is multiplied by 4, divide each side by 4 to undo multiplication.

4k/4 > 24/4

k > 6

The solution is any value greater than 6. 

6. Answer : 

y/2 > -1.5

Because y is divided by 2, multiply each side by 2 to undo division.

2(y/2) > 2(-1.5)

y > -3

7. Answer : 

2m/3 ≤ 6

Because m is multiplied by 2/3, multiply each side by the reciprocal of 2/3, that is 3/2.

(3/2)(2m/3) ≤ (3/2)(6)

m ≤ 9

The solution is any value less than or equal to 9. 

8. Answer : 

-b/10 ≥ -0.11

Because -b is divided by 10, multiply each side by -10 and change ≥ to ≤. 

(-b/10)(-10) ≤ -0.11(-10)

10b/10 ≤ 1.1

b ≤ 1.1

9. Answer : 

10 ≥ -x

-x ≤ 10

Because there is -x, multiply each side by -1 and change ≤ to ≥. 

(-1)(-x) ≥ (-1)(10)

x ≥ -10

The solution is any value greater than or equal to -10.

10. Answer : 

-0.25h > 4.25

Because h is multiplied by -0.25, divide each side by -0.25 and change > to <. 

-0.25h/(-0.25) < 4.25/(-0.25)

h < -17

The solution is any value less than -17. 

11. Answer : 

Let y represent the remaining number of pictures William can take.

21 + y ≤ 25

Because 21 is added to y, subtract 21 from each side to undo the addition.

y ≤ 4

It is not reasonable for William to take a negative or fractional number of pictures. 

So, William could take 0, 1, 2, 3, or 4 more pictures.

12. Answer :

Let m represent the number of additional pounds Josh must lift.

225 + m ≥ 260

Because 225 is added to m, subtract 225 from each side to undo the addition.

m ≥ 35

David lift at least 35 additional pounds to reach his goal.

13. Answer : 

Let y represent the number of smoothies James can buy.

2.50y ≤ 16

Because y is multiplied by 2.50, divide each side by 2.50. The symbol does not change.

y ≤ 6.4 

James can buy only a whole number of smoothies.

So, he can buy 0, 1, 2, 3, 4, 5 or 6 smoothies.  

14. Answer : 

Let k represent the number of 10-ounce servings that one pitcher can fill. 

10k ≤ 78

Because k is multiplied by 10, divide each side by 10 to undo the multiplication. 

10k/10 ≤ 78/10

k ≤ 7.8

Number of 10-ounce servings must be a whole number. 

So, the possible numbers of 10-ounce servings that one pitcher can fill :  

0, 1, 2, 3, 4, 5, 6 or 7

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