Using the simple Perimeter formula we can set up our equation.
[tex]p = 2l + 2w[/tex]
[tex]6x + 14x = 2(2x + 3x - 7) + 2w[/tex]
[tex]20x = 4x + 6x - 14 + 2w[/tex]
[tex]10x = - 14 + 2w[/tex]
[tex]10x + 14 = 2w[/tex]
[tex] 5x + 7 = w[/tex]
Therefore the width is 5x + 7.