Solving One Step Inequalites

Approved & Edited by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Philip Benanti

Philip Benanti

Community Contributor

Quizzes Created: 18 | Total Attempts: 26,587

Questions: 18 | Attempts: 339 | Updated: Mar 1, 2024

Questions

Settings

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Questions and Answers

1.

X / 9 > 10
- A.
  
  X < 90
- B.
  
  X > 90
- C.
  
  X > 1.11
- D.
  
  X > 10
Correct Answer
B. X > 90

Explanation
The correct answer is x > 90 because when we divide x by 9 and the result is greater than 10, it means that x must be greater than 90. If x were less than 90, the result of the division would be less than 10.

Rate this question:
2.

X / 6 > 7
- A.
  
  X > 42
- B.
  
  X > 7
- C.
  
  X > 1.17
- D.
  
  X < 42
Correct Answer
A. X > 42

Explanation
The given inequality states that x divided by 6 is greater than 7. To solve this inequality, we can multiply both sides of the inequality by 6 to isolate x. This gives us x > 42, which means that x is greater than 42. Therefore, the correct answer is x > 42.

Rate this question:

1
0
3.

X / -3 > 2
- A.
  
  X > -6
- B.
  
  X < 2
- C.
  
  X < -6
- D.
  
  X > -0.67
Correct Answer
C. X < -6

Explanation
The given inequality states that x divided by -3 is greater than 2. To solve this inequality, we can multiply both sides by -3, but since we are multiplying by a negative number, the inequality sign will flip. This gives us x < -6, which means that x is less than -6. Therefore, the correct answer is x < -6.

Rate this question:
4.

X / -3 > -8
- A.
  
  X < -8
- B.
  
  X > 2.67
- C.
  
  X > 24
- D.
  
  X < 24
Correct Answer
D. X < 24

Explanation
The given inequality states that x divided by -3 is greater than -8. To solve this inequality, we can multiply both sides by -3, which reverses the inequality sign. Therefore, we get x is less than 24. This means that any value of x that is less than 24 will satisfy the inequality.

Rate this question:
5.

X / -5 > -3
- A.
  
  X < 15
- B.
  
  X < 0.60
- C.
  
  X > -3
- D.
  
  X > 15
Correct Answer
A. X < 15

Explanation
The given inequality states that x divided by -5 is greater than -3. To solve this inequality, we can multiply both sides by -5 to get x by itself. When we multiply both sides by -5, we need to reverse the inequality sign. So, x is less than 15, which means the correct answer is x < 15.

Rate this question:
6.

X / 10 > 3
- A.
  
  X > 0.30
- B.
  
  X < 30
- C.
  
  X > 3
- D.
  
  X > 30
Correct Answer
D. X > 30

Explanation
The correct answer is x > 30 because if we divide both sides of the inequality x / 10 > 3 by 10, we get x > 30. This means that x must be greater than 30 in order for the inequality to be true.

Rate this question:
7.

X / 9 > 9
- A.
  
  X > 1
- B.
  
  X > 81
- C.
  
  X > 9
- D.
  
  X < 81
Correct Answer
B. X > 81

Explanation
The given inequality states that x divided by 9 is greater than 9. To solve this inequality, we can multiply both sides of the inequality by 9, which gives us x is greater than 81. Therefore, the correct answer is x > 81.

Rate this question:
8.

When you multiply both sides of any inequality by a negative number, you need to ________ the inequality symbol.

Correct Answer
flip

Explanation
When you multiply both sides of any inequality by a negative number, you need to flip the inequality symbol. This is because multiplying by a negative number reverses the order of the numbers. For example, if we have the inequality 3 > 2 and we multiply both sides by -1, we get -3 < -2. So, in order to maintain the correct order of the numbers, we need to flip the inequality symbol.

Rate this question:

4
9.

Solve: y - 16 < 12
- A.
  
  Y < -28
- B.
  
  Y > 28
- C.
  
  Y < 28
Correct Answer
C. Y < 28

Explanation
The given inequality is y - 16 < 12. To solve this inequality, we can add 16 to both sides to isolate the variable y. This gives us y < 28, which means that y is less than 28. Therefore, the correct answer is y < 28.

Rate this question:
10.

Write an inequality for "a number minus 14 is more than 35."
- A.
  
  14 - n ≥ 35
- B.
  
  N - 14 ≥ 35
- C.
  
  N - 14 < 35
- D.
  
  N - 14 > 35
Correct Answer
D. N - 14 > 35

Explanation
The correct answer is n - 14 > 35. This inequality represents the statement "a number minus 14 is more than 35." By subtracting 14 from a number (n) and setting it greater than 35, we are expressing that the result of the subtraction is greater than 35.

Rate this question:
11.

Write an inequality for "six times a number is at most 91."
- A.
  
  6k ≤ 91
- B.
  
  6k ≥ 91
- C.
  
  6k < 91
- D.
  
  6k > 91
Correct Answer
A. 6k ≤ 91

Explanation
The inequality 6k ≤ 91 represents the statement "six times a number is at most 91." This means that when the number is multiplied by 6, the result is less than or equal to 91.

Rate this question:
12.

Solve. x - (-4) < 12
- A.
  
  X < 8
- B.
  
  X < 16
- C.
  
  X > 8
- D.
  
  X > 16
Correct Answer
A. X < 8

Explanation
The given inequality is x - (-4) < 12. Simplifying this, we get x + 4 < 12. Subtracting 4 from both sides, we have x < 8. Therefore, the correct answer is x < 8.

Rate this question:
13.

Solve. y - (-3) > -16
- A.
  
  Y < -13
- B.
  
  Y < -19
- C.
  
  Y > -19
- D.
  
  Y > -13
Correct Answer
C. Y > -19

Explanation
The given inequality is y - (-3) > -16. Simplifying this, we get y + 3 > -16. Subtracting 3 from both sides, we have y > -19. Therefore, the correct answer is y > -19.

Rate this question:
14.

Solve. z - 5 ≥ 11
- A.
  
  Z ≥ 6
- B.
  
  Z ≥ 16
- C.
  
  Z ≤ 16
- D.
  
  Z ≥ -6
Correct Answer
B. Z ≥ 16

Explanation
The inequality z - 5 ≥ 11 can be solved by adding 5 to both sides of the inequality, resulting in z ≥ 16. This means that any value of z that is greater than or equal to 16 satisfies the inequality.

Rate this question:
15.

Solve. 6x > 12
- A.
  
  X > -2
- B.
  
  X > -6
- C.
  
  X > 2
- D.
  
  X > 18
Correct Answer
C. X > 2

Explanation
The given inequality is 6x > 12. To solve for x, we divide both sides of the inequality by 6, resulting in x > 2. This means that any value of x that is greater than 2 will satisfy the inequality.

Rate this question:
16.

Solve. 4b > -36
- A.
  
  B > -9
- B.
  
  B < -9
- C.
  
  B > 9
- D.
  
  B < 9
Correct Answer
A. B > -9

Explanation
The given inequality is 4b > -36. To solve this inequality, we divide both sides by 4 (since it is a positive number), giving us b > -9. This means that b is greater than -9.

Rate this question:
17.

Solve. -5k ≤ 20
- A.
  
  K ≤ -4
- B.
  
  K ≥ 4
- C.
  
  K ≤ 4
- D.
  
  K ≥ -4
Correct Answer
D. K ≥ -4

Explanation
The given inequality states that -5k is less than or equal to 20. To solve for k, we need to isolate it on one side of the inequality. By dividing both sides of the inequality by -5, we get k greater than or equal to -4. Therefore, the correct answer is k ≥ -4.

Rate this question:
18.

X / -9 > 4
- A.
  
  X > -36
- B.
  
  X < 4
- C.
  
  X > -0.44
- D.
  
  X < -36
Correct Answer
B. X < 4

Explanation
Let's solve the inequality step by step:Start with �−9>4−9x>4.Multiply both sides by -9. Since we're multiplying by a negative number, the direction of the inequality sign flips.
�<4x<4

Rate this question:

0
0

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
Mar 01, 2024

Quiz Edited by
ProProfs Editorial Team
Nov 20, 2014

Quiz Created by
Philip Benanti

Solving One Step Inequalites

X / 9 > 10

X / 6 > 7

X / -3 > 2

X / -3 > -8

X / -5 > -3

X / 10 > 3

X / 9 > 9

When you multiply both sides of any inequality by a negative number, you need to ________ the inequality symbol.

Solve: y - 16 < 12

Write an inequality for "a number minus 14 is more than 35."

Write an inequality for "six times a number is at most 91."

Solve. x - (-4) < 12

Solve. y - (-3) > -16

Solve. z - 5 ≥ 11

Solve. 6x > 12

Solve. 4b > -36

Solve. -5k ≤ 20

X / -9 > 4