Find the value of x for which the points

Let $A\left(x_{1}, y_{1}\right)=A(x, 2), B\left(x_{2}, y_{2}\right)=B(-3,-4)$ and $C\left(x_{3}, y_{3}\right)=C(7,-5)$. So, the condition for three collinear points is

$x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

$\Rightarrow x(-4+5)-3(-5-2)+7(2+4)=0$

$\Rightarrow x+21+42=0$

$\Rightarrow x=-63$

Hence, x = − 63.