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The option c) x < -24 represents the solution set of the given inequality.
<u>Step-by-step explanation</u>:
The given inequality is −1/4x−12 > −6
<u>To find the solution set :</u>
Keep the x term on one side and constants on other side of the inequality.
-1/4x > -6+12
-1/4x > 6
-x > (64)
-x > 24
Multiply both sides with -1 to remove the negative sign of x.
While multiplying or dividing a negative number in an equality, the inequality sign must be flipped.
⇒ x < -24