Final answer:
No, the inequalities are not equivalent.
Step-by-step explanation:
These two inequalities are not equivalent. Let's solve each one separately to see why:
-6x + 18 < 12:
Subtract 18 from both sides: -6x < -6
Divide by -6, remembering that we need to reverse the inequality sign because we are dividing by a negative number: x > 1
2x - 45 < -2:
Add 45 to both sides: 2x < 43
Divide by 2: x < 21.5
Since the two solutions are different (x > 1 for the first inequality and x < 21.5 for the second inequality), we can conclude that the inequalities are not equivalent.