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?

Rationale

A) 3x - 4 is the expression that represents the length of the rectangle in terms of X.

The length of the rectangle is described as "four less than three times the width". In algebraic terms, "three times the width" translates to 3x (where x is the width), and "four less than" translates to subtracting 4 from that product, giving us the expression 3x - 4.

A (3x - 4) CORRECT

This is the correct answer. It accurately represents the length of the rectangle, as it correctly translates the phrase "four less than three times the width" to algebraic expression. The term "three times the width" is represented by 3x, and "four less than" is represented by subtracting 4 from 3x, which gives us 3x - 4.

B (4x - 3) YOUR ANSWER

This choice incorrectly represents the phrase "four less than three times the width". The term "three times the width" should be represented by 3x, not 4x, and "four less than" should subtract 4, not 3, from that product.

C (4 - 3x) YOUR ANSWER

This choice incorrectly interprets the phrase "four less than three times the width". In this case, the subtraction is reversed, leading to an incorrect value for the length. The term "three times the width" is correctly represented by 3x, but "four less than" should subtract 4 from 3x, not the other way around.

D (3 - 4x) YOUR ANSWER

This choice incorrectly interprets the phrase "four less than three times the width". In this case, both the multiplication and the subtraction are reversed, leading to an incorrect value for the length. The term "three times the width" should be represented by 3x, not 4x, and "four less than" should subtract 4 from 3x, not the other way around.

Conclusion

The correct expression to represent the length of the rectangle in terms of X, when the length is described as "four less than three times the width", is 3x - 4. This expression accurately translates the given phrase into algebraic form. The other choices either misrepresent the multiplication or the subtraction, leading to incorrect representations of the length.

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?

A) 3x - 4 is the expression that represents the length of the rectangle in terms of X.

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