Correct Answer: B

Rationale: To solve the equation x · 7 = x − 36, start by multiplying both sides by 7 to get 7(x · 7) = 7(x − 36), which simplifies to x = 7x − 252. Next, subtract 7x from both sides to get -6x = -252. Finally, divide both sides by -6 to solve for x, which results in x = 42. Therefore, the correct answer is x = 42. Choice A (x = 6), Choice C (x = 4), and Choice D (x = 252) are incorrect as they do not align with the correct solution derived from the equation.

Correct Answer: B

Rationale: To solve the equation x · 7 = x − 36, start by multiplying both sides by 7 to get 7(x · 7) = 7(x − 36), which simplifies to x = 7x − 252. Next, subtract 7x from both sides to get -6x = -252. Finally, divide both sides by -6 to solve for x, which results in x = 42. Therefore, the correct answer is x = 42. Choice A (x = 6), Choice C (x = 4), and Choice D (x = 252) are incorrect as they do not align with the correct solution derived from the equation.

Correct Answer: A

Rationale: To find the discount amount, calculate 20% of $30: 0.20 $30 = $6. Subtract the discount from the original price to get the sale price: $30 - $6 = $24. Therefore, the correct answer is $24. Choices B, C, and D are incorrect as they do not reflect the correct calculation of applying a 20% discount to the original price of $30.

Correct Answer: B

Rationale: To identify the negative value, simplify each expression. A) simplifies to 6 which is positive. B) simplifies to 0 which is neither positive nor negative. C) simplifies to -11 which is negative. D) simplifies to -30 which is negative. Therefore, only choice B results in a non-negative value, making it the correct answer.

Correct Answer: D

Rationale: To calculate Matt's new wage after a 3/20 increase, we need to add this percentage increase to his original wage. The increase in decimal form is 3/20 = 0.15. Therefore, the new wage is w + w(0.15) = w(1 + 0.15) = 1.15w. This means the correct answer is D. Choices A, B, and C are incorrect because they do not account for the full 3/20 increase in the wage. Choice A (0.15w) represents only the increase percentage, not the total new wage. Choice B (0.85w) and Choice C (1.12w) do not accurately calculate the new wage after the increase, leading to incorrect representations of the final wage.