Question

The set of values of $x$ for which the inequality
$(2x+3)(1-x)(x+5)\ge 0\text{holds true is}$

Answer 1

Given :
$(2x+3)(1-x)(x+5)\ge 0$

$\Rightarrow (2x+3)(x-1)(x+5)\le 0$
(Multiplying with - sign changes the inequality)

Zeros of given expressions are

$\Rightarrow x=\frac{-3}{2},1,-5$

Sign scheme is shown in the figure below.

The values of x for which
$(2x+3)(x-1)(x+5)\le 0$
is given from above sign - scheme as,
($-\infty ,-5]\cup [\frac{-3}{2},1]$
Hence the correct answer is Option C.