Question

What property of equality is displayed in step 3 in solving of 9m + 4 - 7m = 5m+7/3

Step 1:
9m + 4 - 7m = 5m+7/3
9m - 7m + 4 = 5m+7/3

Step 2:
2m+4 = 5m+7/3
3(2m + 4) = (5m+7/3)3

Step 3:
6m + 12 = 5m + 7
6m + 12 - 12 = 5m + 7 - 12

Answer 1

In Step 3, the property of equality displayed is the **Subtraction Property of Equality**. This property states that if you subtract the same number from both sides of an equation, the two sides remain equal.

In your example, the operation being performed is subtracting 12 from both sides of the equation:

\[ 6m + 12 - 12 = 5m + 7 - 12 \]

This maintains the equality of the two sides. Specifically, you are simplifying the left side to \( 6m \) and the right side to \( 5m - 5 \).