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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.
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2.
Solve. 13a + 12 = 8a -13
A.
5
B.
-5
C.
1/5
D.
-1/5
Correct Answer B. -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.
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3.
Solve. 16p + 7 = 2p - 7
A.
-2
B.
1
C.
-1
D.
2
Correct Answer C. -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.
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4.
Twice a number is 4 more than the number. Choose the equation to find the unknown; then solve.
A.
2x + 4 = x; x = -4
B.
2x + x = 4; x = 4/3
C.
2x = x + 4; x = 4
D.
2x = x + 4; x = -2
Correct Answer C. 2x = x + 4; x = 4
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.
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5.
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 the unknown number, we can determine if the result is greater than 35.
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6.
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 you multiply a number by 6, the result is less than or equal to 91.
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7.
If h = 2, which word describes the inequality 6h + 9 < 20?
A.
Open
B.
True
C.
False
D.
Addition
Correct Answer C. False
Explanation The inequality 6h + 9 < 20 is false when h = 2. By substituting h = 2 into the inequality, we get 6(2) + 9 < 20, which simplifies to 12 + 9 < 20, and further simplifies to 21 < 20. This statement is false, as 21 is not less than 20. Therefore, the correct answer is false.
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8.
Charles and Betty spent more than $230 while shopping. Betty spent $138. Choose the inequality that shows what Charles spent.
A.
C > $108
B.
C < $92
C.
C = $92
D.
C > $92
Correct Answer D. 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.
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9.
Solve. x - (-4) < 12
A.
X < 8
B.
X < 16
C.
X > 8
D.
X > 16
Correct Answer A. X < 8
Explanation To solve the inequality x - (-4) < 12, we can simplify it by adding 4 to both sides of the inequality. This gives us x < 8 as the solution. This means that any value of x that is less than 8 will satisfy the inequality.
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10.
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.
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11.
Solve. z - 5 ≥ 11
A.
Z ≥ 6
B.
Z ≥ 16
C.
Z ≤ 16
D.
Z ≥ -6
Correct Answer B. Z ≥ 16
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.
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12.
Solve. 6x > 12
A.
X > -2
B.
X > -6
C.
X > 2
D.
X > 18
Correct Answer C. X > 2
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.
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13.
Solve. 4b > -36
A.
B > -9
B.
B < -9
C.
B > 9
D.
B < 9
Correct Answer A. 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.
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14.
Solve. -5k ≤ 20
A.
K ≤ -4
B.
K ≥ 4
C.
K ≤ 4
D.
K ≥ -4
Correct Answer D. 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.
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15.
Solve. d > 3 -7
A.
D > -21
B.
D < 21
C.
D < -21
D.
D > 21
Correct Answer C. D < -21
Explanation The inequality d > 3 indicates that d is greater than 3. The inequality d < -21 means that d is less than -21. Therefore, the correct answer is d < -21, as it aligns with the given information.
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16.
Solve. 5x - 10 > 20
A.
X < 6
B.
X > 2
C.
X < 2
D.
X > 6
Correct Answer D. 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.
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17.
Solve. -7p - 5 < -33
A.
P > -4
B.
P < 5.14
C.
P > 4
D.
P < 5
Correct Answer C. P > 4
Explanation The given inequality is -7p - 5 < -33. To solve it, we need to isolate the variable p. Adding 5 to both sides gives -7p < -28. Dividing both sides by -7 (and flipping the inequality sign since we are dividing by a negative number) gives p > 4. Therefore, the correct answer is p > 4.
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18.
Solve. x - 6 < 9 2
A.
X < -30
B.
X < 30
C.
X > 30
D.
X > -30
Correct Answer B. X < 30
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 < 30.
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19.
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?
Correct Answer 180
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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20.
Find the number of miles traveled by driving at 50 miles per hour for 4 1/2 hours.
Correct Answer 225
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.