Answer: The correct option is
(D) x < 1.
Step-by-step explanation: We are given to find the solution to the following inequality :
\(-6x+5>-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We will be using the following property of inequalities :
\(a>b~~~~~~\Rightarrow -a<-b.\)
The solution of equation (i) is as follows :
\(-6x+5>-1\\\\\Rightarrow -6x>-1-5\\\\\Rightarrow -6x>-6\\\\\Rightarrow 6x<6\\\\\Rightarrow x<\dfrac{6}{6}\\\\\Rightarrow x<1.\)
Thus, the required solution is x < 1.
Option (D) is CORRECT.
