0\ \ \ and\ \ \ \ \ 2x-7>0\\.\ \ \ \ \ \ 5x>-2\ \ \ \ \ \ and\ \ \ \ \ 2x>7\\.\ \ \ \ \ \ \ x>-\frac{2}{5}\ \ \ \ \ \ and\ \ \ \ \ \ x>3 \frac{1}{2} \\\\D=(3 \frac{1}{2};\ +\infty)\\\\Ans.\ \ The\ width\ is\ \ \ \ 2x-7"> 10 x 2 − 31 x − 14 = 10 x 2 + 4 x − 35 x − 14 = 2 x ( 5 x + 2 ) − 7 ( 5 x + 2 ) = = ( 5 x + 2 ) ( 2 x − 7 ) D : 5 x + 2 > 0 an d 2 x − 7 > 0 . 5 x > − 2 an d 2 x > 7 . x > − 5 2 an d x > 3 2 1 D = ( 3 2 1 ; + ∞ ) A n s . T h e w i d t h i s 2 x − 7
The width of the rectangle can be found using the area and length formula. After simplifying the trinomial for the area, we get the expression for the width as W = 2 x − 7 . This expression holds as long as 5 x + 2 = 0 .
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