# Solving One Step Inequalites

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| By Philip Benanti
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Philip Benanti
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Quizzes Created: 18 | Total Attempts: 27,123
Questions: 18 | Attempts: 339

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• 1.

### X / 9 > 10

• A.

X < 90

• B.

X > 90

• C.

X > 1.11

• D.

X > 10

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.

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• 2.

### X / 6 > 7

• A.

X > 42

• B.

X > 7

• C.

X > 1.17

• D.

X < 42

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.

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• 3.

### X / -3 > 2

• A.

X > -6

• B.

X < 2

• C.

X < -6

• D.

X > -0.67

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.

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• 4.

### X / -3 > -8

• A.

X < -8

• B.

X > 2.67

• C.

X > 24

• D.

X < 24

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.

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• 5.

### X / -5 > -3

• A.

X < 15

• B.

X < 0.60

• C.

X > -3

• D.

X > 15

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.

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• 6.

### X / 10 > 3

• A.

X > 0.30

• B.

X < 30

• C.

X > 3

• D.

X > 30

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.

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• 7.

### X / 9 > 9

• A.

X > 1

• B.

X > 81

• C.

X > 9

• D.

X < 81

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.

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• 8.

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

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.

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• 9.

### Solve:  y - 16 < 12

• A.

Y < -28

• B.

Y > 28

• C.

Y < 28

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.

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• 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

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.

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• 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

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.

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• 12.

### Solve.  x - (-4) < 12

• A.

X < 8

• B.

X < 16

• C.

X > 8

• D.

X > 16

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.

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• 13.

### Solve.  y - (-3) > -16

• A.

Y < -13

• B.

Y < -19

• C.

Y > -19

• D.

Y > -13

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.

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• 14.

### Solve.  z - 5 ≥ 11

• A.

Z ≥ 6

• B.

Z ≥ 16

• C.

Z ≤ 16

• D.

Z ≥ -6

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.

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• 15.

### Solve.  6x > 12

• A.

X > -2

• B.

X > -6

• C.

X > 2

• D.

X > 18

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.

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• 16.

### Solve.  4b > -36

• A.

B > -9

• B.

B < -9

• C.

B > 9

• D.

B < 9

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.

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• 17.

### Solve.  -5k ≤ 20

• A.

K ≤ -4

• B.

K ≥ 4

• C.

K ≤ 4

• D.

K ≥ -4

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.

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• 18.

### X / -9 > 4

• A.

X > -36

• B.

X < 4

• C.

X > -0.44

• D.

X < -36

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

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• Current Version
• Mar 01, 2024
Quiz Edited by
ProProfs Editorial Team
• Nov 20, 2014
Quiz Created by
Philip Benanti

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