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?

Rationale

2(x - 4) = 12

This equation accurately represents the phrase "twice the difference of a number and four is twelve," where the unknown number is denoted by x. The expression inside the parentheses, (x - 4), captures the difference between the number and four, which is then multiplied by 2 to indicate "twice" this difference.

A (2x - 4 = 12) YOUR ANSWER

This equation incorrectly states that twice the number x minus four equals twelve. It fails to account for the critical step of finding the difference between the number and four before applying the multiplication, thus misrepresenting the original phrase.

B (2(x - 4) = 12) CORRECT

This is the correct choice because it sets up the equation to find the difference between the unknown number x and four, which is then multiplied by two. This structure directly aligns with the statement given in the question, making it the appropriate equation to solve for the unknown number.

C (x - 4 = (2)(12)) YOUR ANSWER

This equation incorrectly equates the difference between x and four to the product of two and twelve. It neglects to represent the "twice" aspect of the original statement and incorrectly assumes a direct comparison rather than setting up an equation involving multiplication of the difference.

D ((2)(x) - (2)(4) = (2)(12)) YOUR ANSWER

While this equation uses multiplication, it incorrectly breaks down the components. The left side represents twice the number and twice four but does not reflect the requirement of finding the difference first. This approach does not capture the essence of the problem as stated.

Conclusion

In conclusion, the equation 2(x - 4) = 12 accurately represents the original statement about the unknown number and four. It captures both the operation of finding the difference and the requirement to double that difference before equating it to twelve. The other options fail to maintain the correct mathematical relationship as described in the problem.

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?

2(x - 4) = 12

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