Answer: The correct option is (A) x ≥ −0.25.
Step-by-step explanation: We are given to solve the following inequality :
[tex]-8x\leq2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following property of inequalities :
[tex]a\leq b~~~~~~~~~\Rightarrow -a\geq -b.[/tex]
From inequality (i), we get
[tex]-8x\leq 2\\\\\Rightarrow -(-8x)\geq-2~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using the above property}]\\\\\Rightarrow 8x\geq -2\\\\\Rightarrow x\geq\dfrac{-2}{8}\\\\\Rightarrow x\geq -0.25.[/tex]
Thus, the required solution is x ≥ −0.25.
Option (A) is CORRECT.
