1.
X / 9 > 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.
2.
X / 6 > 7
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.
3.
X / -3 > 2
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.
4.
X / -3 > -8
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.
5.
X / -5 > -3
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.
6.
X / 10 > 3
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.
7.
X / 9 > 9
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.
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.
9.
Solve: y - 16 < 12
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.
10.
Write an inequality for "a number minus 14 is more than 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.
11.
Write an inequality for "six times a number is at most 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.
12.
Solve. x - (-4) < 12
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.
13.
Solve. y - (-3) > -16
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.
14.
Solve. z - 5 ≥ 11
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.
15.
Solve. 6x > 12
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.
16.
Solve. 4b > -36
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.
17.
Solve. -5k ≤ 20
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.
18.
X / -9 > 4
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