An advertisement poster in the window of a shoe store is in the shape of a rectangle. The length of the poster is 9 less than 4 × the width. Which expression represents the length of the poster when w is the width

Rationale

4w - 9 represents the length of the poster when w is the width.

In this problem, the length of the poster is defined as being 9 less than 4 times the width (w). Therefore, the expression that accurately reflects this relationship is 4w - 9.

A (4w - 9) CORRECT

This expression correctly represents the length of the poster based on the given relationship. It is derived from the problem statement, where the length is specified as 4 times the width minus 9, thus confirming its accuracy.

B (9 - 4w) YOUR ANSWER

This expression suggests that the length is 9 minus 4 times the width, which incorrectly reverses the relationship stated in the question. Instead of being a positive multiple of the width, it inaccurately implies a decrease based on the width, which does not align with the problem.

C (4w + 9) YOUR ANSWER

This expression indicates that the length is 4 times the width plus 9, which contradicts the original statement of the length being less than the calculated width. This misinterpretation results in an incorrect representation of the relationship.

D (9w - 4) YOUR ANSWER

This expression implies that the length is 9 times the width minus 4, which is entirely unrelated to the stated relationship. It does not represent any part of the problem correctly and introduces a different coefficient and constant.

Conclusion

The length of the poster is defined as 9 less than 4 times the width, making 4w - 9 the correct expression for this relationship. The other choices either misinterpret the problem’s conditions or introduce incorrect values, confirming that A is the only valid expression for the length based on the given width.

An advertisement poster in the window of a shoe store is in the shape of a rectangle. The length of the poster is 9 less than 4 × the width. Which expression represents the length of the poster when w is the width

4w - 9 represents the length of the poster when w is the width.

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