Question

What is the solution to the inequality? −6x+5>−1

​ x>1 ​

​ x<−1 ​

​ x>−1 ​

​ x<1 ​

Answer 1

$-6x+5>-1\implies -6x>-6\implies x<1$

Answer 2

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.