23. Sam was told that twice the difference of a number and four is twelve. If x stands for the unknown number which equation could Sam solve to find the number?
Answer: D
Sam can solve the equation (2)(x) - (2)(4) = (2)(12) to find the unknown number.
This equation correctly represents the statement that twice the difference of a number and four is twelve.
A) 2x - 4 = 12
This option is incorrect because it does not accurately reflect the relationship described in the problem. The equation suggests that two times the number minus four equals twelve, rather than focusing on the difference between the number and four.
B) 2(x - 9) = 12
This option is incorrect as it alters the original relationship. The equation implies that the difference between the number and nine is being multiplied by two, which does not correspond to the problem's stipulation regarding the number and four.
C) x - 4 = (2)(12)
This option is incorrect because it sets the difference between the number and four equal to twenty-four, rather than addressing the requirement that twice the difference of the number and four equals twelve.
D) (2)(x) - (2)(4) = (2)(12)
This option is correct as it directly translates the problem statement into a mathematical equation. It accurately represents the expression "twice the difference of a number and four" by distributing the two correctly.
Conclusion
Option D is definitively correct as it captures the essence of the problem by setting up the equation that Sam can solve. All other options misinterpret the relationship between the number and four, leading to incorrect equations that do not align with the original statement.