Solving Inequalities Pre-algebra Quiz! Trivia

1. Find the number of miles traveled by driving at 50 miles per hour for 4 1/2 hours.

To find the number of miles traveled, we need to multiply the speed (50 miles per hour) by the time (4 1/2 hours). Multiplying 50 by 4 gives us 200, and multiplying 50 by 1/2 gives us 25. Adding these two results together, we get a total of 225 miles traveled.

Explanation

To find the number of miles traveled, we need to multiply the speed (50 miles per hour) by the time (4 1/2 hours). Multiplying 50 by 4 gives us 200, and multiplying 50 by 1/2 gives us 25. Adding these two results together, we get a total of 225 miles traveled.

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2. Green Valley Middle School is selling wrapping paper. For each roll of wrapping paper sold the school receives 45 cents. How many rolls of wrapping paper must be sold to reach their goal of at least $81?

To find the number of rolls of wrapping paper needed to reach the goal of at least $81, we can set up the equation: 0.45x ≥ 81, where x is the number of rolls. By dividing both sides of the inequality by 0.45, we get x ≥ 180. This means that the school must sell at least 180 rolls of wrapping paper to reach their goal of $81 or more.

Explanation

To find the number of rolls of wrapping paper needed to reach the goal of at least $81, we can set up the equation: 0.45x ≥ 81, where x is the number of rolls. By dividing both sides of the inequality by 0.45, we get x ≥ 180. This means that the school must sell at least 180 rolls of wrapping paper to reach their goal of $81 or more.

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3. Solve. z - 5 ≥ 11

Z ≥ 6

Z ≥ 16

Z ≤ 16

Z ≥ -6

The correct answer is z ≥ 16 because when we subtract 5 from both sides of the inequality z - 5 ≥ 11, we get z ≥ 16. This means that z must be greater than or equal to 16 in order for the inequality to be true.

Explanation

The correct answer is z ≥ 16 because when we subtract 5 from both sides of the inequality z - 5 ≥ 11, we get z ≥ 16. This means that z must be greater than or equal to 16 in order for the inequality to be true.

4. Solve. 6x > 12

X > -2

X > -6

X > 2

X > 18

The correct answer is x > 2 because when we divide both sides of the inequality 6x > 12 by 6, we get x > 2. This means that any value of x that is greater than 2 will satisfy the inequality.

Explanation

The correct answer is x > 2 because when we divide both sides of the inequality 6x > 12 by 6, we get x > 2. This means that any value of x that is greater than 2 will satisfy the inequality.

5. Solve. x - 6 < 9 2

X < -30

X < 30

X > 30

X > -30

The given inequality states that x minus 6 is less than 9. To solve for x, we can add 6 to both sides of the inequality, resulting in x being less than 15. Therefore, the correct answer is x

Explanation

The given inequality states that x minus 6 is less than 9. To solve for x, we can add 6 to both sides of the inequality, resulting in x being less than 15. Therefore, the correct answer is x

6. Solve. 2m + 2 = 4m

2

0

-2

1

To solve the equation 2m + 2 = 4m, we need to isolate the variable m. We can do this by subtracting 2m from both sides of the equation. This gives us 2 = 2m. Then, we divide both sides of the equation by 2 to solve for m. The result is 1, which means that m = 1 is the solution to the equation.

Explanation

To solve the equation 2m + 2 = 4m, we need to isolate the variable m. We can do this by subtracting 2m from both sides of the equation. This gives us 2 = 2m. Then, we divide both sides of the equation by 2 to solve for m. The result is 1, which means that m = 1 is the solution to the equation.

7. 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 the unknown number, we can determine if the result 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 the unknown number, we can determine if the result is greater than 35.

8. Solve. 13a + 12 = 8a -13

5

-5

1/5

-1/5

To solve the equation 13a + 12 = 8a - 13, we need to isolate the variable "a" on one side of the equation. First, we can combine like terms by subtracting 8a from both sides, which gives us 5a + 12 = -13. Then, we can subtract 12 from both sides to get 5a = -25. Finally, we divide both sides by 5 to solve for "a", which gives us a = -5. Therefore, the correct answer is -5.

Explanation

To solve the equation 13a + 12 = 8a - 13, we need to isolate the variable "a" on one side of the equation. First, we can combine like terms by subtracting 8a from both sides, which gives us 5a + 12 = -13. Then, we can subtract 12 from both sides to get 5a = -25. Finally, we divide both sides by 5 to solve for "a", which gives us a = -5. Therefore, the correct answer is -5.

9. If h = 2, which word describes the inequality 6h + 9 < 20?

Open

True

False

Addition

The inequality 6h + 9

Explanation

The inequality 6h + 9

10. Solve. -7p - 5 < -33

P > -4

P < 5.14

P > 4

P < 5

The given inequality is -7p - 5 4. Therefore, the correct answer is p > 4.

Explanation

The given inequality is -7p - 5 4. Therefore, the correct answer is p > 4.

11. Solve. -5k ≤ 20

K ≤ -4

K ≥ 4

K ≤ 4

K ≥ -4

The given inequality is -5k ≤ 20. To solve this inequality, we divide both sides by -5, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us k ≥ -4. Therefore, the correct answer is k ≥ -4.

Explanation

The given inequality is -5k ≤ 20. To solve this inequality, we divide both sides by -5, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us k ≥ -4. Therefore, the correct answer is k ≥ -4.

12. Solve. 16p + 7 = 2p - 7

-2

1

-1

2

To solve the equation 16p + 7 = 2p - 7, we need to isolate the variable p. First, we can subtract 2p from both sides of the equation to eliminate the variable on the right side. This gives us 14p + 7 = -7. Next, we can subtract 7 from both sides to get rid of the constant term on the left side. This leaves us with 14p = -14. Finally, we divide both sides by 14 to solve for p, giving us p = -1.

Explanation

To solve the equation 16p + 7 = 2p - 7, we need to isolate the variable p. First, we can subtract 2p from both sides of the equation to eliminate the variable on the right side. This gives us 14p + 7 = -7. Next, we can subtract 7 from both sides to get rid of the constant term on the left side. This leaves us with 14p = -14. Finally, we divide both sides by 14 to solve for p, giving us p = -1.

13. Solve. 5x - 10 > 20

X < 6

X > 2

X < 2

X > 6

The given inequality is 5x - 10 > 20. To solve this, we add 10 to both sides to isolate the variable: 5x > 30. Then, we divide both sides by 5 to solve for x: x > 6. Therefore, the correct answer is x > 6.

Explanation

The given inequality is 5x - 10 > 20. To solve this, we add 10 to both sides to isolate the variable: 5x > 30. Then, we divide both sides by 5 to solve for x: x > 6. Therefore, the correct answer is x > 6.

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

X < 8

X < 16

X > 8

X > 16

To solve the inequality x - (-4)

Explanation

To solve the inequality x - (-4)

15. 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 you multiply a number 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 you multiply a number by 6, the result is less than or equal to 91.

16. 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.

17. Solve. 4b > -36

B > -9

B < -9

B > 9

B < 9

The inequality 4b > -36 can be solved by dividing both sides of the inequality by 4. This gives us b > -9, which means that b is greater than -9. Therefore, the correct answer is b > -9.

Explanation

The inequality 4b > -36 can be solved by dividing both sides of the inequality by 4. This gives us b > -9, which means that b is greater than -9. Therefore, the correct answer is b > -9.

18. Twice a number is 4 more than the number. Choose the equation to find the unknown; then solve.

2x + 4 = x; x = -4

2x + x = 4; x = 4/3

2x = x + 4; x = 4

2x = x + 4; x = -2

The equation 2x = x + 4 is the correct equation to find the unknown. This is because the problem states that twice a number is 4 more than the number. By setting up the equation 2x = x + 4, we are saying that twice the number (2x) is equal to the number (x) plus 4. Solving this equation, we find that x = 4, which satisfies the given condition.

Explanation

The equation 2x = x + 4 is the correct equation to find the unknown. This is because the problem states that twice a number is 4 more than the number. By setting up the equation 2x = x + 4, we are saying that twice the number (2x) is equal to the number (x) plus 4. Solving this equation, we find that x = 4, which satisfies the given condition.

19. Charles and Betty spent more than $230 while shopping. Betty spent $138. Choose the inequality that shows what Charles spent.

C > $108

C < $92

C = $92

C > $92

Based on the information given, Betty spent $138, which means that the total amount spent by both Charles and Betty is greater than $230. Since Charles spent an amount greater than $92, the correct inequality is c > $92.

Explanation

Based on the information given, Betty spent $138, which means that the total amount spent by both Charles and Betty is greater than $230. Since Charles spent an amount greater than $92, the correct inequality is c > $92.

20. Solve. d > 3 -7

D > -21

D < 21

D < -21

D > 21

The inequality d > 3 indicates that d is greater than 3. The inequality d

Explanation

The inequality d > 3 indicates that d is greater than 3. The inequality d