SOLVING INEQUALITIES BY MULTIPLYING OR DIVIDING WORKSHEET

Problem 1 : 

Solve the following inequality and graph the solution. 

3x < 18

Problem 2 : 

Solve the following inequality and graph the solution. 

y/2 > -1.5

Problem 3 : 

Solve the following inequality and explain your solution in words. 

4k > 24

Problem 4 : 

Solve the following inequality and explain your solution in words. 

2m/3 ≤ 6

Problem 5 : 

Solve the following inequality and graph the solution. 

-10a > 15

Problem 6 : 

Solve the following inequality and graph the solution. 

-b/10 ≥ -0.11

Problem 7 : 

Solve the following inequality and explain your solution in words.

Problem 8 : 

Solve the following inequality and explain your solution in words.

Problem 9 :

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 10 :

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

Problem 11 :

Solve the inequality and graph the solution

-2n - 40 < 5(6 + n) + 7n

Problem 12 :

Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.?

Problem 13 :

Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

Problem 14 :

Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal?

Detailed Answer Key

1. Answer : 

3x < 18

Because x is multiplied by 3, divide each side by 3 to undo the multiplication.

3x/3 < 18/3

x < 6

2. 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

3. 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. 

4. 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. 

5. Answer : 

-10a > 15

Because a is multiplied by -10, divide each side by -10 and change > to <. 

-10a/(-10) < 15/(-10)

a < -1.5

6. 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

7. 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.

8. 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. 

9. 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.  

10. 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

11. Answer : 

-2n - 40 < 5(6 + n) + 7n

Distributing 5, we get

-2n - 40 < 30 + 5n + 7n

-2n - 40 < 30 + 12n

Subtracting 12n on both sides, we get

-2n - 12n - 40 < 30

Adding 40 on both sides

-14n < 30 + 40

-14n < 70

Dividing by -14 on both sides, we get

n < -5

12. Answer :

Number of weeks he cuts = x

Weight should be reduced lesser than 175 lbs

Current weight = 200 lbs

200 - 2x < 175

Subtracting 200 on both sides

-2x < 175 - 200

-2x < -25

Dividing by -2 on both sides.

x > 25/2

x > 12.5

So, more than 12.5 weeks.

13. Answer :

Profit of 5.50 per bag.

Let x be the number of bags.

5.50 x ≥ 5525

Dividing by 5.50, we get

x ≥ 5525 / 5.50

x ≥ 950

They need to sell 950 bags.

14. Answer :

At least 12 hours. So, ≥ 12

0.75 hours. Let x be the number of more sessions remain for her to meet.

3 + 0.75x ≥ 12

Subtracting 3 on both sides

0.75x ≥ 12 - 3

0.75x ≥ 9

Dividing by 0.75, we get

x ≥ 9/0.75

x ≥ 12

Atleast more than 12 more sessions.

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