Mathematics

Question

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

​ x>1 ​

​ x<−1 ​

​ x>−1 ​

​ x<1 ​








2 Answer

  • [tex]-6x+5>-1\implies -6x>-6\implies x<1[/tex]
  • Answer:  The correct option is

    (D) x < 1.

    Step-by-step explanation:  We are given to find the solution to the following inequality :

    [tex]-6x+5>-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

    We will be using the following property of inequalities :

    [tex]a>b~~~~~~\Rightarrow -a<-b.[/tex]

    The solution of equation (i) is as follows :

    [tex]-6x+5>-1\\\\\Rightarrow -6x>-1-5\\\\\Rightarrow -6x>-6\\\\\Rightarrow 6x<6\\\\\Rightarrow x<\dfrac{6}{6}\\\\\Rightarrow x<1.[/tex]

    Thus, the required solution is x < 1.

    Option (D) is CORRECT.

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