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.