Question

Step 1:9m+4−7m=5m+739m−7m+4=5m+73Step 2:2m+4=5m+733(2m+4)=(5m+73)3Step 3:6m+12=5m+76m+12−12=5m+7−12Step 4:6m=5m−56m−5m=5m−5m−5m=−5(1 point)ResponsesSubtraction Property of EqualitySubtraction Property of EqualityMultiplication Property of EqualityMultiplication Property of EqualityDivision Property of EqualityDivision Property of EqualityAddition Property of Equality

Answer 1

Let's break down the steps of your solution and identify the properties being used.

**Step 1:**
You started with the equation:
\[ 9m + 4 - 7m = 5m + 73m - 7m + 4 \]
And simplified it to:
\[ 2m + 4 = 5m + 7 \]
In this step, you combined like terms. You aren't explicitly applying a property of equality here, but just simplifying.

**Step 2:**
You multiplied both sides of the equation by 3:
\[ 3(2m + 4) = 3(5m + 7) \]
This step uses the **Multiplication Property of Equality**, which states that if two expressions are equal, multiplying both sides by the same number keeps them equal.

**Step 3:**
You now have:
\[ 6m + 12 = 15m + 21 \]
You then subtract 12 from both sides to isolate terms involving \( m \):
\[ 6m = 15m + 21 - 12 \]
This simplified to:
\[ 6m = 15m + 9 \]
In this step, you use the **Subtraction Property of Equality** by subtracting the same number (12) from both sides.

**Step 4:**
Then you had:
\[ 6m - 15m = 9 \]
Which simplifies to:
\[ -9m = 9 \]
Dividing both sides by -9 gives
\[ m = -1 \]
Here, you used the **Division Property of Equality**.

In summary:

- In **Step 2**, you used the **Multiplication Property of Equality**.
- In **Step 3**, you used the **Subtraction Property of Equality**.
- In **Step 4**, you used the **Division Property of Equality**.

If you have particular multiple-choice options for each step, you could match these actions to the corresponding properties from your list:

- **Subtraction Property of Equality** for Step 3.
- **Multiplication Property of Equality** for Step 2.
- **Division Property of Equality** for the final step.