Answer: x-2y > 3
Step-by-step explanation:
By the given diagram,
The related line of the inequality is passes through the point (0,-1.5) and (3,0)
Thus, the equation of the related line,
[tex]y-(-1.5)=\frac{0-(-1.5)}{(3-0)} (x-0)[/tex]
[tex]y+1.5=\frac{(0+1.5)}{3}x[/tex]
[tex]y+1.5=\frac{1.5}{3}x[/tex]
[tex]y+\frac{15}{10}=\frac{15}{30}x[/tex]
[tex]y+\frac{3}{2}=\frac{1}{2}x[/tex]
[tex]\frac{2y+3}{2}=\frac{1}{2}x[/tex]
[tex]2y+3=x\implies 2y+3-x=0\implies -x+2y=-3\implies x-2y=3 [/tex]
Thus, the related line of the given inequality is x-2y=3
Hence, the possible inequalities are,
x-2y ≥ 3, x-2y ≤ 3, x-2y > 3 or x-2y < 3
By the given diagram,
The inequality does not contains the origin,
Thus, the possible inequalities are x-2y ≥ 3 or x-2y > 3.
Again,
The doted line shows that the inequality does not contain the equal sign.
Hence, the inequality is,
x-2y > 3
⇒ First option is correct.
