Solve the equation for the unknown. 3x + 2 = 20

Correct Answer: C

Rationale: In the given equation 3x + 2 = 20, the correct answer is x = 6. To solve this equation, we need to isolate the variable x. First, we subtract 2 from both sides to get 3x = 18. Then, we divide by 3 on both sides to find x = 6. Option A) x = 2: This is incorrect because if we substitute x = 2 back into the original equation, we get 3(2) + 2 = 8, not 20. Option B) x = 4: This is incorrect as well. Substituting x = 4 back into the equation gives us 3(4) + 2 = 14, not 20. Option D) x = 8: This is incorrect. If we substitute x = 8 into the equation, we get 3(8) + 2 = 26, not 20. Educationally, this problem tests the student's understanding of solving linear equations. By following the correct steps of isolating the variable, students can arrive at the correct solution. Understanding the properties of equality and the order of operations are crucial in solving such equations accurately. Practicing similar problems can help reinforce these concepts and improve problem-solving skills.

Correct Answer: C

Rationale: To solve for x, add 5 to both sides of the equation: 3x - 5 + 5 = 16 + 5, which simplifies to 3x = 21. Next, divide both sides by 3: x = 21 · 3 = 7. Therefore, the correct answer is x = 7, making option A the correct choice. Option C, '8,' is incorrect as it is not the solution obtained from the correct calculations. Options B and D, '5' and '9,' are also incorrect and not the solution to the given equation.

Correct Answer: C

Rationale: To find the mean of a data set, you add up all the values and then divide by the total number of values. In this case, the sum of the data set is 185. Dividing this sum by the total number of values (12) gives you a mean of 16. Therefore, the correct answer is 16. Choice A (14.25), Choice B (15.25), and Choice D (17) are incorrect because they do not accurately represent the average value of the given data set.

Correct Answer: A

Rationale: To multiply fractions, you multiply the numerators to get the new numerator and multiply the denominators to get the new denominator. Therefore, multiplying 2/3 by 3/4 results in (2*3) / (3*4) = 6/12. Simplifying 6/12 by dividing both the numerator and denominator by 6 gives 1. Hence, the correct answer is 1. Choices B, C, and D are incorrect as they do not represent the correct product of multiplying 2/3 by 3/4.

Correct Answer: A

Rationale: Rationale: In this question, the correct answer is A) 2. When dividing 8 by 4, you are essentially looking for how many times 4 can fit into 8. By dividing 8 by 4, you get 2, because 4 goes into 8 two times evenly. Option B) 4 is incorrect because dividing 8 by 4 does not result in 4, but rather 2. Option C) 6 is incorrect as well, as it is not a valid result of dividing 8 by 4. Option D) 8 is also incorrect because when dividing a number by itself, the result is always 1, not 8. Educationally, understanding basic arithmetic operations like division is crucial for solving math problems accurately. Dividing numbers helps in understanding the concept of sharing or distributing quantities equally. It is essential for building a strong foundation in mathematics, which is necessary for various real-life applications and higher-level math concepts. Therefore, mastering these fundamental operations is key to success in mathematics.