In Step 1, you correctly applied the distributive property to expand the left side of the inequality:
\[ -6(3w - 7) < -66 \implies -18w + 42 < -66 \]
In Step 2, you are simplifying the inequality by subtracting 42 from both sides. The property of inequality being used here is the Addition (or Subtraction) Property of Inequality, which states that if you add or subtract the same value from both sides of an inequality, the inequality remains valid.
So, from Step 1 to Step 2, you correctly used this property to rewrite the inequality:
\[ -18w + 42 - 42 > -66 - 42 \]
This simplifies to:
\[ -18w > -108 \]
Now, you have the simplified inequality ready for further steps (note that you had a small mistake in your notation; it should remain \(-18w > -108\) instead of \(-17w > -108\)).
Next, you would proceed to divide both sides by -18 to solve for \(w\), remembering that dividing by a negative number reverses the inequality sign.
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