Error analysis

a student says that the perimeter of a rectangle with side lengths (2x-1) inches and 3x inches can be written as (10x-1) inches. because 2 (2x-1) + 2 (3x) = 10x-1. explain why this statement is incorrect.

One side (l) = 2x-1

other side (w) = 3x

perimiter = all of the sides added together

perimiter = 2l + 2w

perimiter = 2 (2x-1) + 2 (3x)

2 (2x) - 2 (1) + 2 (3x) = 4x - 2 + 6x

perimiter = 10x - 2

The previous statement is incorrect because the student did not distribute the 2 onto the - 1.

2 (2x-1) + 2 (3x) = 4x-2+6x = 10x - 2 & not = 10x-1