Answer:
Option A, Option D and Option E are correct options.
Step-by-step explanation:
We need to find solutions of the inequality: [tex]2x^2-1>6x[/tex]
We will check the options and see, which options satisfy the inequality.
Option A
x=-4
Put x=-4
[tex]2x^2-1>6x\\2(-4)^2-1>6(-4)\\2(16)-1>-24\\32-1>-24\\31>-24\:\:True[/tex]
So, x=-4 is the solution of inequality.
Option B
x=3
Put x=-3
[tex]2x^2-1>6x\\2(3)^2-1>6(3)\\2(9)-1>18\\18-1>18\\17>18\:\:False[/tex]
So, x=3 is not the solution of inequality.
Option C
x=1
Put x=1
[tex]2x^2-1>6x\\2(1)^2-1>6(1)\\2(1)-1>6\\2-1>6\\1>6\:\:False[/tex]
So, x=1 is not the solution of inequality.
Option D
x=5
Put x=5
[tex]2x^2-1>6x\\2(5)^2-1>6(5)\\2(25)-1>30\\50-1>30\\49>30\:\:True[/tex]
So, x=5 is the solution of inequality.
Option E
x=-2
Put x=-2
[tex]2x^2-1>6x\\2(-2)^2-1>6(-2)\\2(4)-1>-12\\8-1>-12\\7>-12\:\:True[/tex]
So, x=-2 is the solution of inequality.
So, Option A, Option D and Option E are correct options.
