I am trying to find the quadrants for the following question:
In the rectangular co-ordinate system, which quadrants contain at least one point $(x, y)$ that satisfies the inequality:
$$2y > \dfrac x5$$
$(A.) \\$ I
$(B.)\\$ II
$(C.)\\$ III
$(D.)$ IV
How do I go about it ?
$$2y\gt \dfrac x5 \implies 10y \gt x$$
If $x,y$ in $1$ quadrant , $x,y \gt0$ there exists many $x,y$ with the desired property.
If $x,y$ in $2$ quadrant , $x\lt0 , y\gt 0$ there exists many $x,y$ with the desired property.
If $x,y$ in $3$ quadrant , $ x\lt 0 , y\lt 0$ there exists many $x,y$ with the desired property.
If $x,y$ in $4$ quadrant ,$x\gt 0 , y \lt 0$ there do not exists any $x,y$ with the desired property.
So the answer is $1,2,3$ quadrants.