40. Sam was told that twice the difference of a number and four is twelve. If x x x stands for the unknown number, which equation could Sam solve to find the number?
Answer: B
2(x - 4) = 12
To find the unknown number, Sam needs to set up an equation that reflects the statement "twice the difference of a number and four is twelve." The correct equation is 2(x - 4) = 12, which accurately captures the relationship described.
A) 2x - 4 = 12
This equation is incorrect because it does not represent the "difference of a number and four." Instead, it implies that twice the number minus four equals twelve, which does not align with the problem statement.
B) 2(x - 4) = 12
This option is correct as it directly translates the verbal statement into a mathematical equation. It indicates that Sam should double the difference between the unknown number and four to equal twelve.
C) x - 4 = (2)(12)
This equation is incorrect because it suggests that the difference between the unknown number and four is equal to twenty-four, which misrepresents the original statement. The problem specifically involves doubling the difference, not equating it directly to another number.
D) (2)(x) - (2)(4) = (2)(12)
While this equation seems to involve the correct elements, it complicates the expression unnecessarily. It indicates twice the number minus eight equals twenty-four, which does not reflect the original statement about the difference from four.
Conclusion
The equation 2(x - 4) = 12 accurately represents the statement about doubling the difference between the unknown number and four. All other options misinterpret or misrepresent the relationship described in the problem, making them invalid choices for solving for the unknown number.