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To solve the inequality −4x−5<31, we can begin by isolating the variable x on one side of the inequality.
Adding 5 to both sides of the inequality, we get:
−4x−5+5<31+5
−4x<36
Now, dividing both sides of the inequality by -4 (remembering to flip the inequality sign because we are dividing by a negative number), we get:
x>-9
So, the solution set for the inequality −4x−5<31 is x>-9.