what property on inequality can justify the math in step 2?

Question

Step 1: -6(3w-7)>-66
-18w + 42> -66
step 2: -18w+42-42> -66 - 42
18w> -108
step 3: -18w/-18 > -108/-18

Answer 1

In step 2 of the inequality transformation, you are applying the Subtraction Property of Inequality. This property states that if you subtract the same number from both sides of an inequality, the inequality remains valid.

In your case:

1. You started with \(-18w + 42 > -66\).
2. You then subtracted \(42\) from both sides: \[ -18w + 42 - 42 > -66 - 42 \] which simplifies to: \[ -18w > -108 \]

So, the property that justifies the transition from step 1 to step 2 is indeed the Subtraction Property of Inequality.