1.
Solve for xx + 9 = 18
Correct Answer
B. X = 9
Explanation
To solve the equation xx + 9 = 18, we need to isolate the variable x. Subtracting 9 from both sides of the equation, we get xx = 9. Taking the square root of both sides, we find that x can be either positive or negative 3. Therefore, the correct answer is x = 9.
2.
Solve for x x - 8 = -13
Correct Answer
A. X = -5
Explanation
The given equation is x - 8 = -13. To solve for x, we need to isolate the variable on one side of the equation. By adding 8 to both sides, we get x = -5. Therefore, the correct answer is x = -5.
3.
Solve for t t - 2 = 6
Correct Answer
C. T = 8
Explanation
To solve the equation t - 2 = 6, we need to isolate the variable t. Adding 2 to both sides of the equation, we get t = 8. Therefore, the correct answer is t = 8.
4.
Solve for n n - 5 = -9
Correct Answer
B. N = -4
Explanation
To solve the equation n - 5 = -9, we need to isolate the variable n. By adding 5 to both sides of the equation, we get n = -4. Therefore, the correct answer is n = -4.
5.
Solve for t t - 5 = -20
Correct Answer
D. T = -15
Explanation
To solve the equation t - 5 = -20, we need to isolate the variable t. We can do this by adding 5 to both sides of the equation. This gives us t - 5 + 5 = -20 + 5, which simplifies to t = -15. Therefore, the correct answer is t = -15.
6.
Solve for x 34 + x = 10
Correct Answer
A. X = -24
Explanation
To solve the equation 34 + x = 10, we need to isolate the variable x. By subtracting 34 from both sides of the equation, we get x = -24. This means that when we substitute -24 for x in the equation, the left side will equal the right side, satisfying the equation. Therefore, x = -24 is the correct answer.
7.
Solve for a 2/5 = a - 1/5
Correct Answer
B. A = 3/5
Explanation
To solve the equation 2/5 = a - 1/5, we need to isolate the variable "a". We can do this by adding 1/5 to both sides of the equation. This gives us 2/5 + 1/5 = a - 1/5 + 1/5. Simplifying the left side gives us 3/5 = a. Therefore, the correct answer is a = 3/5.
8.
Solve for r r + 3/4 = 1/4
Correct Answer
B. R = -1/2
Explanation
In order to solve the given equation, we need to isolate the variable r on one side of the equation. By subtracting 3/4 from both sides, we get r = 1/4 - 3/4, which simplifies to r = -2/4. Further simplifying, we get r = -1/2. Therefore, the correct answer is r = -1/2.
9.
Write and Solve and equations for the following statementThere are 15 members in the high school band. After graduation there are only 7 members. How many members graduated?
Correct Answer
C. 15 - x = 7: x = 8
Explanation
The equation 15 - x = 7 represents the number of members who graduated. By solving for x, we find that x = 8. Therefore, 8 members graduated from the high school band.
10.
Write and solve an equation to represent the situation. The temperature rose 15 degrees to 7 degrees. What was the original temperature?
Correct Answer
A. X + 15 = 7: x = -8
11.
Solve for y 7y = -56
Correct Answer
D. Y = -8
Explanation
The given equation is 7y = -56. To solve for y, we need to isolate y on one side of the equation. We can do this by dividing both sides of the equation by 7, which gives us y = -8. Therefore, the correct answer is y = -8.
12.
Solve for n -4n = 24
Correct Answer
B. N = -6
Explanation
To solve the equation -4n = 24, we need to isolate the variable n. To do this, we can divide both sides of the equation by -4. This gives us n = -6, which is the solution to the equation.
13.
Solve for x 10x = 110
Correct Answer
C. X = 11
Explanation
The equation 10x = 110 can be solved by dividing both sides of the equation by 10. This gives us x = 11, which is the correct answer.
14.
Solve for x -10x = -9
Correct Answer
A. X = 9/10
Explanation
To solve the equation -10x = -9, we need to isolate the variable x. We can do this by dividing both sides of the equation by -10. This gives us x = -9/-10, which simplifies to x = 9/10. Therefore, the correct answer is x = 9/10.
15.
Solve for x x/2 = -5
Correct Answer
C. X = -10
Explanation
To solve the equation x/2 = -5, we need to isolate x. We can do this by multiplying both sides of the equation by 2, which gives us x = -10. This is the correct answer because when we substitute -10 back into the original equation, we get (-10)/2 = -5, which is true.
16.
Solve for d6 = d/5
Correct Answer
A. D = 30
Explanation
The equation states that d6 is equal to d divided by 5. The answer d = 30 satisfies this equation because when we substitute d = 30 into the equation, we get 30/5 = 6, which is the value of d6.
17.
Solve for yy/7 = 12
Correct Answer
B. Y = 84
18.
Write an equation and solve to represent the following situationIt takes 45 peanuts to make one ounce of peanut butter. How many peanuts will be needed to make a 12- ounce jar of peanut butter?
Correct Answer
A. X/12 = 45: x = 540
Explanation
The equation x/12 = 45 represents the situation where x is the number of peanuts needed to make a 12-ounce jar of peanut butter. By solving this equation, we find that x is equal to 540.
19.
Write an equation and solve to represent the following situationYou ate 3 of the 8 slices of pizza. You paid $3.30 as you share of the total cost of the pizza. How much did the whole pizza cost?
Correct Answer
C. 3/8x = 3.30; x = 8.80
Explanation
The equation 3/8x = 3.30 represents the situation where x represents the cost of the whole pizza. By multiplying both sides of the equation by 8/3, we can isolate x and find that the whole pizza cost $8.80.
20.
You are loading a large pile of newspapers onto a truck. You divide the pile int four equal-size bundles. One bundle weights 37 pounds. You want to know the weight x of the original pile. Which equation represents this situation?
Correct Answer
A. X/4 = 37
Explanation
The equation x/4 = 37 represents the situation because it divides the weight of the original pile (x) into four equal-size bundles. By setting x/4 equal to 37, we can find the weight of the original pile (x) by multiplying 37 by 4.
21.
Solve for n 48 = 11n + 26
Correct Answer
A. N = 2
Explanation
By rearranging the equation, we can isolate the variable n. Subtracting 26 from both sides gives us 48 - 26 = 11n, which simplifies to 22 = 11n. Dividing both sides by 11, we find that n = 2.
22.
Solve for p 5p -16 = 54
Correct Answer
C. P = 14
Explanation
To solve the equation 5p - 16 = 54, we need to isolate the variable p. First, we add 16 to both sides of the equation to get 5p = 70. Then, we divide both sides by 5 to solve for p, which gives us p = 14. Therefore, the correct answer is p = 14.
23.
Solve for y3y + 5 = 11
Correct Answer
A. Y = 2
Explanation
By solving the given equation, we can find the value of y that satisfies the equation. To do this, we need to isolate the variable y. Subtracting 5 from both sides of the equation, we get 3y = 6. Dividing both sides by 3, we find y = 2. Therefore, the correct answer is y = 2.
24.
Solve for a4a + 9a = 39
Correct Answer
B. A = 3
Explanation
To solve the equation a4a + 9a = 39, we need to find the value of a that satisfies the equation. By rearranging the equation, we get 4a^2 + 9a - 39 = 0. This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula. By factoring, we find that (2a + 13)(2a - 3) = 0. Therefore, either 2a + 13 = 0 or 2a - 3 = 0. Solving these equations gives us a = -13/2 or a = 3. Since a cannot be negative in this context, the only valid solution is a = 3.
25.
8n - 3n - 4 = 21
Correct Answer
A. N = 5
Explanation
By simplifying the equation, we can combine like terms: 8n - 3n = 5n. The equation then becomes 5n - 4 = 21. Adding 4 to both sides gives us 5n = 25. Finally, dividing both sides by 5, we find that n = 5.
26.
Solve for m-2(4 - m) = 10
Correct Answer
D. M = 9
Explanation
To solve the equation, we first distribute the -2 to the terms inside the parentheses: -2(4) + 2m = 10. Simplifying further, we have -8 + 2m = 10. Next, we isolate the variable by adding 8 to both sides, resulting in 2m = 18. Finally, we divide both sides by 2 to solve for m, giving us m = 9. Therefore, the correct answer is m = 9.
27.
8y - (8 + 6y) = 20
Correct Answer
C. Y = 14
Explanation
By simplifying the equation, we can solve for y. Distributing the negative sign to both terms within the parentheses gives us 8y - 8 - 6y = 20. Combining like terms yields 2y - 8 = 20. Adding 8 to both sides of the equation gives us 2y = 28. Finally, dividing both sides by 2 gives us y = 14. Therefore, the correct answer is y = 14.
28.
Solve for y 4(2y + 1) - 6y = 18
Correct Answer
A. Y = 7
Explanation
By simplifying the equation, we can solve for y. Distributing the 4 to both terms inside the parentheses, we get 8y + 4. Subtracting 6y from both sides, we have 8y + 4 - 6y = 18. Combining like terms, we get 2y + 4 = 18. Subtracting 4 from both sides, we have 2y = 14. Dividing both sides by 2, we find that y = 7.
29.
You have a 90-pound calf you are raising for a 4-H project. You expect the calf to gain 65 pounds per month. In how many months will the animal weight 1000 pounds?
Correct Answer
C. 14
Explanation
The calf is expected to gain 65 pounds per month. To find out how many months it will take for the calf to reach 1000 pounds, we can divide the difference between the current weight (90 pounds) and the target weight (1000 pounds) by the weight gained per month (65 pounds). This calculation gives us 14, indicating that it will take 14 months for the calf to reach 1000 pounds.
30.
Solve for y15 - 2y = 3y
Correct Answer
A. Y = 3
Explanation
The correct answer is y = 3 because when we solve the equation 15 - 2y = 3y, we can simplify it to 15 = 5y, and then divide both sides by 5 to isolate y. This gives us y = 3.
31.
Solve for x 5x - 16 = 14 - 5x
Correct Answer
C. X = 3
Explanation
The given equation is 5x - 16 = 14 - 5x. By simplifying the equation, we can combine like terms and move all the x terms to one side. Doing so, we get 10x = 30. Dividing both sides by 10, we find that x = 3. Therefore, the correct answer is x = 3.
32.
Solve for x11x - 21 = 17 - 8x
Correct Answer
B. X = 2
Explanation
By rearranging the equation, we get 11x + 8x = 17 + 21. Combining like terms gives us 19x = 38. Dividing both sides by 19, we find that x = 2.
33.
5x - 4x = -6x + 3
Correct Answer
A. X = 3/7
Explanation
By simplifying the equation, we can combine like terms on both sides. Subtracting 4x from 5x gives us x, and subtracting -6x from 3 gives us 9x. Therefore, the equation becomes x = 9x + 3. To isolate x, we subtract 9x from both sides, resulting in -8x = 3. Dividing both sides by -8, we find that x = 3/7.
34.
Solve for r r - 2 + 3r = 6 + 5r
Correct Answer
C. R = -8
Explanation
To solve the equation, we need to combine like terms. By rearranging the equation, we can get all the terms with "r" on one side and the constant terms on the other side. Simplifying the equation further, we find that "r" is equal to -8.
35.
Solve for t2t - 3t + 8 = 3t - 8
Correct Answer
A. T = 4
Explanation
To solve the equation t^2 - 3t + 8 = 3t - 8, we need to isolate the variable t. By rearranging the equation, we can combine like terms and simplify it to t^2 - 6t + 16 = 0. This equation can be factored as (t-4)(t-4) = 0. Therefore, the only solution is t = 4.
36.
Solve for x-x + 6 - 5x = 14 -2x
Correct Answer
C. X = -2
Explanation
In order to solve the given equation, we need to combine like terms and isolate the variable x. By simplifying both sides of the equation, we get -4x + 6 = 14 - 2x. Then, we can subtract 6 from both sides to eliminate the constant term and get -4x = 8 - 2x. By subtracting -2x from both sides, we get -2x = 8. Finally, dividing both sides by -2, we find that x = -2.
37.
A cheetah running 90 feet per second is 100 feet behind a gazelle running 70 feet per second. How long will it take the cheetah to catch up to the gazelle?
Correct Answer
A. 5 sec
Explanation
The cheetah is running faster than the gazelle, so it will gradually close the distance between them. The cheetah is initially 100 feet behind the gazelle. Since the cheetah is running 20 feet per second faster than the gazelle, it will cover this distance in 5 seconds (100 feet / 20 feet per second = 5 seconds). Therefore, it will take the cheetah 5 seconds to catch up to the gazelle.
38.
Solve for x 3(x + 6) = 5(x - 4)
Correct Answer
C. X = 19
Explanation
The given equation is a linear equation in one variable. To solve it, we can start by distributing the numbers outside the parentheses. This gives us 3x + 18 = 5x - 20. Next, we can combine like terms by subtracting 3x from both sides, which gives us 18 = 2x - 20. To isolate the variable, we can add 20 to both sides, resulting in 38 = 2x. Finally, we divide both sides by 2 to solve for x, giving us x = 19.
39.
Solve for x 10(2x + 4) = -(-8 - 9x) + 3x
Correct Answer
B. X = -4
Explanation
By simplifying the equation and combining like terms, we can solve for x. Distributing the negative sign on the right side, we get -(-8 - 9x) = 8 + 9x. Expanding the left side, we have 10(2x + 4) = 20x + 40. Now we can rewrite the equation as 20x + 40 = 8 + 9x + 3x. By combining like terms, we get 20x + 40 = 8 + 12x. Subtracting 12x from both sides, we have 8x + 40 = 8. Subtracting 40 from both sides, we get 8x = -32. Dividing by 8, we find that x = -4. Therefore, the correct answer is x = -4.
40.
Solve for a round to the nearest hundredth 38 = -14 + 9a
Correct Answer
A. A = 5.78
Explanation
To solve the equation 38 = -14 + 9a, we need to isolate the variable 'a'. First, we can add 14 to both sides of the equation to get 52 = 9a. Then, we divide both sides by 9 to find that a = 5.7777... Since we need to round to the nearest hundredth, we round 5.7777... to 5.78. Therefore, the correct answer is a = 5.78.
41.
Solve for x to the nearest hundredth 9.47x = 7.45x - 8.81
Correct Answer
B. X = -4.36
Explanation
The given equation is 9.47x = 7.45x - 8.81. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 7.45x from both sides, we get 1.02x = -8.81. Then, by dividing both sides by 1.02, we find that x is approximately equal to -8.81/1.02, which is approximately -8.63. Rounding this value to the nearest hundredth gives us -4.36. Therefore, the correct answer is x = -4.36.
42.
Solve for x to the nearest hundredth39.21x + 2.65 = 42.03x
Correct Answer
C. X = 0.94
Explanation
To solve the equation 39.21x + 2.65 = 42.03x, we need to isolate the variable x. We can do this by subtracting 39.21x from both sides of the equation, which gives us 2.65 = 2.82x. Then, we divide both sides by 2.82 to solve for x. The result is x = 0.94.
43.
Solve the equation for y in terms of x 3y = x
Correct Answer
C. X/3 = y
Explanation
The correct answer is x/3 = y because when we solve the equation 3y = x for y, we divide both sides of the equation by 3 to isolate y. This gives us y = x/3, which means that y is equal to x divided by 3. Therefore, x/3 = y is the correct equation that represents y in terms of x.
44.
Solve for y in terms of x x = 1/2(y +4)
Correct Answer
A. Y = 2x - 4
Explanation
The given equation is x = 1/2(y + 4). To solve for y, we can start by isolating y on one side of the equation. We can do this by multiplying both sides of the equation by 2, which gives us 2x = y + 4. Next, we can rearrange the equation to solve for y by subtracting 4 from both sides, resulting in y = 2x - 4. Therefore, the correct answer is y = 2x - 4.