Answer
$(3x-7) \text{ inches}$
Work Step by Step
Using $A=lw$ or the forumula for the area of a rectangle, then
\begin{array}{l}\require{cancel}
A=lw
\\\\
15x^2-29x-14=(5x+2)w
\\\\
\dfrac{15x^2-29x-14}{5x+2}=w
\\\\
w=\dfrac{(5x+2)(3x-7)}{5x+2}
\\\\
w=\dfrac{(\cancel{5x+2})(3x-7)}{\cancel{5x+2}}
\\\\
w=3x-7
.\end{array}
Hence, the width is $
(3x-7) \text{ inches}
.$
