1. Solve 3x – 19 = 2
Ax = -17
Bx = -17/3
Cx = 7
Dx = -51
Ex = 20
Fx = 18
2. Solve 4x + 12x = 62 + 4(11)
Ax = 7
Bx = 5
Cx = 35
Dx = 64
Ex = 11
Fx = 7/2
3. Solve 8x – 7 = x + 10
Ano solution
Bx = 1/3
Cx = 1/10
Dx = 3/7
Ex = 17/7
Fx = 17/9
4. Solve 4(5x – 9) = -2(3x + 7)
Ax = 8/13
Bx = 7/2
Cx = -11/7
Dx = 11/13
Ex = 11/3
Fx = -4/5
5. Solve d = m/v for m
Am = vd
Bm = d/v
Cm = v/d
Dm = d + v
Em = v - d2
Fm = 1/vd
6. Solve V = lwh for w
Aw = V – lh
Bw = l/h
Cw = vlh
Dw = v + l + h
Ew = 1/vh
FW = V/(lh)
7. Solve A = ½bh for h
Ah = ½Ab
Bh = 2A/b
Ch = A - 2b
Dh = A2b2
Eh = A2/b
Fh = b/2A
8. Examine the following solution to a linear equation. Do you see a mistake? Identify the first line of the solution that is incorrect (if any).
Original Equation: 7x + 42 = 12x – 8
Solution:
ANo mistakes.
Bstep 4
Cstep 2
Dstep 1
Estep 5
Fstep 3
9. Examine the following solution to a linear equation. Do you see a mistake? Identify the first line of the solution that is incorrect (if any).
Original Equation: -3(x – 9) = ½(4x + 12)
Solution:
Astep 3
Bstep 5
Cstep 2
Dstep 1
Estep 4
Fno mistakes
10. Examine the following solution to a linear equation. Do you see a mistake? Identify the first line of the solution that is incorrect (if any).
Original Equation: 30x = 23(1 + 3) + 12x + 22
Solution:
Ano mistakes
Bstep 5
Cstep 3
Dstep 6
Estep 1
Fstep 4
11. Examine the following solution to a linear equation. Do you see a mistake? Identify the first line of the solution that is incorrect (if any).
Original Equation: 15x + 12 – 8x = -3 + 7x - 7
Solution:
Ano mistakes
Bstep 5
Cstep 1
Dstep 4
Estep 2
Fstep 3
12. Anne is seven years older than her brother, Brandon. Anne is 23. Which equation below could you solve to determine Brandon’s age? (Let A represent Anne’s age and let B represent Brandon’s age.)
AA + B + 7 = 23
BB = 7 + 23
CA + B = 23
D23 = B + 7
EA = 23 + 7
F23 = A + 7
13. Last Friday, the Cougars beat the Tigers in basketball by 17 points. The Tigers scored 62 points. Which equation below could you solve to find out how many points the Cougars scored? (Let C represent the Cougars' score and let T represent the Tigers' score.)
AT + 17 = 62 + C
BT + C = 62
CC – 17 = 62
DTC = 62
EC = 62 - T
FT - 17 = 62
14. Of the 62 points scored by the Tigers, Mary scored 28 points, which is twice as many points as Lashawna scored. Which of the following equations describes the number of points scored by Lashawna? (Let M represent the points Mary scored and let L represent the points Lashawna scored.)
A2L = 62 - M
BM/2 = 62L
CM - 2L = 28
D2L = 28
EL = 62 - 2M
FM - 2 = 28
15. Joey owns a small bakery and today Phoebe has ordered 100 cookies. If Joey boxes the cookies by the dozen, which of the following equations describes how many boxes of cookies Phoebe will have? Let b represent the number of boxes. (HINT: All of the cookie boxes are not necessarily full.)
A100 = b/12
B12b + 4 = 100
C12b = 100 – 4
D100/b = 12
E(100-4)/12=b-1
F12 + b = 100
16. As Gary is preparing to move, he notices that several of his smaller packed boxes will fit inside a large one. If each of the smaller boxes is a cube with side length 9 inches, and the volume of the larger box is 19683 cubic inches, which equation could be used to determine n, the number of smaller boxes that will fit inside the larger one?
A19683/9 = n
B19683 = n * 81
C19683 = 729n
D19683 - 729 = n
E19683 * 9 = n
F19683 = 9n
17. Newton’s second law states that the amount of force acting on an object is equal to the product of the mass of the object and the acceleration of the object (F = ma). Which of the following equations is the correct way to solve this equation for m?
Am = Fa
Bm = F - a
Cm = F + a
Dm = a/F
Em = 1/(Fa)
Fm = F/a
18. The formula F = C(9/5) + 32 may be used to convert a temperature in degrees Celsius to degrees Fahrenheit. How could this equation be rearranged to convert a temperature in degrees Fahrenheit to degrees Celsius?
AC = (5/9)(F - 32)
BC = 32F - 9/5
CC = (5/9)F + 32
DC = (9/5) - 32F
EC = 32F - (9/5)
F5C = F/9 -32
19. Malachi is an artist with unrecognized talent. As he plans to create the masterpiece that will cause him to be discovered, he realizes that he needs more paint. He will need to purchase several new colors, each of which costs $7.50. In addition, he will have to pay 6% sales tax. Which equation below could Malachi use to decide how many colors he can buy for $45.00?
A(7.50)(6)c = 45.00
B(7.50)c = 45.00(1.6)
C(7.50 + 0.06)c = 45.00
D(7.50)(1.06)c = 45.00
E(7.50)c = (45.00)(0.06)
F(7.50)c = (45.00)(1.06)
20. At a local candy store, Malcolm purchased some 25-cent candies and some 30-cent candies. He spent a total of $4.75. Which equation below describes the number of each type of candy he bought?
A25x + 30y = 4.75
Bx + y = (4.75)/(0.25 + 0.30)
C25 + x + 30 + y = 475
D0.25/x + 0.30/y = 4.75
Ex + y = 4.75 - 0.25 - 0.30
F0.25x + 0.30y = 4.75
2 d
4 c
5 f
6 b
7 a
20 b
sorry i forgot to put those in before i submitted it.. they are there now.. sorry
I checked the first 10.
Numbers 1 and 3 are correct.
Numbers 2, 4, 5, 6 are wrong.
I don't know about 7.
In numbers 8, 9, and 10, no steps were posted.
I only checked 7 and 20..both are wrong.
Interesting work done here.
Anyone got number 19??
1. To solve the equation 3x - 19 = 2, we can start by isolating the variable x. First, add 19 to both sides of the equation to get 3x = 21. Then, divide both sides by 3 to solve for x, giving us x = 7. So, the correct answer is Cx = 7.
2. To solve the equation 4x + 12x = 62 + 4(11), we can simplify both sides of the equation. Starting with the left side, we have 16x. On the right side, 4(11) can be calculated as 44. So the equation becomes 16x = 62 + 44. Combining the terms on the right side, we get 16x = 106. To solve for x, divide both sides by 16, and we find that x = 6.625. So, none of the given options for this problem is the correct answer.
3. To solve the equation 8x - 7 = x + 10, we can start by isolating the variable x. First, subtract x from both sides of the equation to get 7x - 7 = 10. Then, add 7 to both sides to get 7x = 17. Finally, divide both sides by 7 to solve for x, giving us x = 2.42857, which is approximately 2.43. So, none of the given options for this problem is the correct answer.
4. To solve the equation 4(5x - 9) = -2(3x + 7), we can start by distributing the coefficients. On the left side, 4 multiplied by 5x gives us 20x, and 4 multiplied by -9 gives us -36. On the right side, -2 multiplied by 3x gives us -6x, and -2 multiplied by 7 gives us -14. The equation becomes 20x - 36 = -6x - 14. To simplify further, we can add 6x to both sides to move all x terms to one side of the equation. This gives us 26x - 36 = -14. Next, add 36 to both sides to get 26x = 22. Finally, divide both sides by 26 to solve for x, giving us x = 0.84615, which is approximately 0.85. So, none of the given options for this problem is the correct answer.
5. The equation d = m/v represents the relationship between density (d), mass (m), and volume (v). To solve for m, we need to isolate the variable on one side of the equation. To do this, we can multiply both sides of the equation by v, giving us dv = m. So, the correct answer is Bm = d/v.
6. The equation V = lwh represents the formula for the volume (V) of a rectangular prism or box, with length (l), width (w), and height (h). To solve for w, we need to isolate the variable on one side of the equation. Dividing both sides of the equation by lh gives us V/lh = w. So, the correct answer is FW = V/(lh).
7. The equation A = 1/2bh represents the formula for finding the area (A) of a triangle, with base (b) and height (h). To solve for h, we need to isolate the variable on one side of the equation. Multiplying both sides of the equation by 2 gives us 2A = bh. Finally, dividing both sides by b gives us 2A/b = h. So, the correct answer is Bh = 2A/b.
8. To determine if there is a mistake in the given solution, we need to examine the steps and check for errors. Without the specific steps provided, it is not possible to identify the incorrect line. So, none of the given options for this problem is the correct answer.
9. To determine if there is a mistake in the given solution, we need to examine the steps and check for errors. Without the specific steps provided, it is not possible to identify the incorrect line. So, none of the given options for this problem is the correct answer.
10. To determine if there is a mistake in the given solution, we need to examine the steps and check for errors. Without the specific steps provided, it is not possible to identify the incorrect line. So, none of the given options for this problem is the correct answer.
11. To determine if there is a mistake in the given solution, we need to examine the steps and check for errors. Without the specific steps provided, it is not possible to identify the incorrect line. So, none of the given options for this problem is the correct answer.
12. If Anne is seven years older than her brother Brandon, and Anne is 23, we can set up the equation A = B + 7 to represent their ages. Substituting 23 for A, the equation becomes 23 = B + 7. To solve for B, we subtract 7 from both sides of the equation, giving us B = 16. So, the correct answer is BB = 7 + 23.
13. If the Cougars beat the Tigers by 17 points and the Tigers scored 62 points, we can set up the equation C = 62 + 17 to find out how many points the Cougars scored. Adding 62 and 17, we get C = 79. So, the correct answer is BT + C = 62.
14. If Mary scored twice as many points as Lashawna, and Mary scored 28 points, we can set up the equation M = 2L to describe their scores. Substituting 28 for M, the equation becomes 28 = 2L. To solve for L, we divide both sides of the equation by 2, giving us L = 14. So, the correct answer is DM = 28.
15. If Joey boxes the cookies by the dozen, we can set up the equation b = 100/12 to determine how many boxes Phoebe will have. 100/12 is equal to 8.333, so the correct answer is None of the given options.
1 c
2 b
3 a
4 b
5 d
6 a
7 e
8 e
9 d
10 d
11 a
12 a
13 d
14 f
15 e
16 c
17 b
18 d
19 f
20 e