5. If X represents the width of a rectangle and the length is four less than three × the width, which of the following expressions represents the length of the rectangle in terms of X?
Answer: A
The length of the rectangle in terms of X is represented by the expression 3X - 4.
The length of the rectangle can be expressed as three times the width (X) minus four, which is mathematically represented by the expression 3X - 4.
A) 3x - 4
This option is correct because it accurately reflects the relationship described in the question. The length is defined as four less than three times the width, which translates to the expression 3X - 4.
B) 4x - 3
This option is incorrect because it suggests that the length is four times the width minus three, which does not align with the original description of the relationship between length and width.
C) 4 - 3x
This option is also incorrect because it implies that the length is derived by subtracting three times the width from four, which misrepresents the relationship stated in the question.
D) 3 - 4x
This option is incorrect as well, indicating a negative relationship where length is three minus four times the width, which is contrary to the problem's specifications regarding the length being based on three times the width.
Conclusion
The expression 3X - 4 accurately represents the length of the rectangle as it follows the mathematical relationship laid out in the question. The other options fail to correctly depict the relationship between the width and length, making them invalid representations of the length in terms of X.