SOLVING INEQUALITIES BY ADDING OR SUBTRACTING WORKSHEET

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 :

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 6 :

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 7 :

The NGA hoped to raise more than $3000 for cancer. Every time a student donated $40 they would get to pie a math teacher in the face. How many donations would it take for the students to reach or exceed their goal?

Problem 8 :

Beth wanted to go to the school dance but only had $25 to spend. If the ticket cost $5 how many cookies could Beth buy at the dance if each cookie costs $1.25?

Problem 9 :

George wanted to start his own painting business. He bought a ladder and some supplies for $180. He plans on charging $10 per hour painting. How many hours will George have to work if he is to make at least a profit of $750?

Problem 10 :

Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Write an inequality to determine the minimum number of whole days it will take for him to be able to spell at least 75 words.

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 : 

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

Solve :

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 graph the nonnegative integers less than or equal to 4.

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

Look Back : 

Adding 0, 1, 2, 3, or 4 more pictures will not exceed 25.

6. Answer :

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

Solve :

225 + m ≥ 260

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

m ≥ 35

Look Back : 

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

7. Answer :

Fund to be raised = more than 3000

So, we have to use > 3000

Amount that each student is donating = $40

Let x be the number of donation.

40x > 3000

We have to divide by 40 on both sides.

x > 3000/40

x > 75

So, it would take more than 75 students to donate.

8. Answer :

Let x be the number of cookies.

Cost of each cookie = 1.25

Amount he has to spend = $25

Cost of ticket = 5

5 + 1.25x < 25

Subtracting 5 on both sides

1.25x < 25 - 5

1.25x < 20

Dividing by 1.25, we get

x < 20/1.25

x < 16

So, Beth can buy 16 or less than 16 cookies.

9. Answer :

Let x be the number of hours he works.

Cost of ladder = $180

Charge per hour for painting = $10

He should get the profit at least 750, then we have to use the inequality sign ≥.

-180 + 10x ≥ 750

Adding 180 on both sides,

10x ≥ 750 + 180

10x ≥ 930

x ≥ 930/10

x ≥ 93

So, George should work at least 93 hours.

10. Answer :

Let x be the required number of days.

At least 75 words, so we have to use the inequality sign ≥.

10 + 2x ≥ 75

Subtracting 10 on both sides

2x ≥ 75 - 10

2x ≥ 65

Dividing by 2, we get 

x ≥ 65/2

x ≥ 32.5

So,  Peter able to spend 33 days.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.