"the perimeter of a rectangle is 42 centimeters. the length of the rectangle can be represented by (x+4), and the width can be represented by (2x-7). what are the dimensions of this rectangle in centimeters"

Perimeter is the sum of all the sides. One length equals (x+4) so both of the lengths will equal 2(x+4) = 2x+8. One width is (2x-7) so both will equal 2(2x-7) = 4x-14.

we can write this into an equation like so:
2x+8+4x-14=42
6x-6=42
6x=48
x=8

Then we substitute 8 back into the equations for the lengths of the sides.
8+4= 12 so the length is 12cm
2x8= 16, 16-7=9 so the width is 9cm

Where’s the problems ? ?