Solving One Step Inequalites

1) X / 9 > 9

X > 1

X > 81

X > 9

X < 81

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.

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.

2) Solve. z - 5 ≥ 11

Z ≥ 6

Z ≥ 16

Z ≤ 16

Z ≥ -6

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.

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.

3) X / 6 > 7

X > 42

X > 7

X > 1.17

X < 42

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.

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.

4) Solve. 6x > 12

X > -2

X > -6

X > 2

X > 18

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.

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.

5) X / 9 > 10

X < 90

X > 90

X > 1.11

X > 10

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.

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.

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

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.

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.

Submit

7) Solve: y - 16 < 12

Y < -28

Y > 28

Y < 28

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.

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.

8) X / -5 > -3

X < 15

X < 0.60

X > -3

X > 15

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.

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.

9) X / 10 > 3

X > 0.30

X < 30

X > 3

X > 30

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.

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.

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

14 - n ≥ 35

N - 14 ≥ 35

N - 14 < 35

N - 14 > 35

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.

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.

11) X / -3 > 2

X > -6

X < 2

X < -6

X > -0.67

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.

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.

12) X / -3 > -8

X < -8

X > 2.67

X > 24

X < 24

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.

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.

13) Solve. x - (-4) < 12

X < 8

X < 16

X > 8

X > 16

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.

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.

14) Solve. 4b > -36

B > -9

B < -9

B > 9

B < 9

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.

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.

15) X / -9 > 4

X > -36

X < 4

X > -0.44

X < -36

Let's solve the inequality step by step:

Start with $\frac{�}{- 9} > 4$ .
Multiply both sides by -9. Since we're multiplying by a negative number, the direction of the inequality sign flips.
$� < 4$

Explanation

Let's solve the inequality step by step:

Start with $\frac{�}{- 9} > 4$ .
Multiply both sides by -9. Since we're multiplying by a negative number, the direction of the inequality sign flips.
$� < 4$

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

6k ≤ 91

6k ≥ 91

6k < 91

6k > 91

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.

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.

17) Solve. y - (-3) > -16

Y < -13

Y < -19

Y > -19

Y > -13

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.

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.

18) Solve. -5k ≤ 20

K ≤ -4

K ≥ 4

K ≤ 4

K ≥ -4

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.

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.