[tex]2(n-2)<3n-6[/tex]
↝ Multiply 2 inside (n-2) as we get 2n-4
[tex]2n-4<3n-6[/tex]
↝ Inequality is almost the same as equation so you just do the same like equation.
[tex]2n-4-3n+6<0\\-n+2<0\\-n<-2[/tex]
↝ Since it's Inequality. When the variable is negative, you have to make it positive.
[tex]n<\frac{-2}{-1}\\n<2[/tex]
↝ BUT! n < 2 isn't the right answer.
↝ Because for Inequality. Taking out the negative/Move the negative variable to another side ( from -n to n and -2 to -2/-1 = 2).
↝ You have to swap the inequality symbol after taking the off the negative variable.
↝ For example, if it is -n < 2 then the answer will be n > -2
or -n < -3 then the answer will be n > 3
But if it is n>2-3 as we get n>-1, not n < -1 because the variable isn't negative at all.
Basically, we swap the inequality symbol when it's negative variable.
↝ Therefore, it's not n < 2 but it is n > 2
So the right choice is n > 2 also known as the ( D ) answer.
