Question

solve the equation. what is the value of m? there are several ways to start solving this equation. there are variables on both sides, and a number on the left side only. so, one way to start is to get all of the variables on one side, and keep the number on the other side. which move can you make to move all of the m terms to the right, while keeping the equation balanced? 5 + 2m = 7m subtract 5 from both sides add 2m to both sides subtract 2m from both sides

Explanation:

Step1: Analyze the goal

We need to move all \( m \)-terms to the right side. The left side has \( 2m \), and the right side has \( 7m \). To eliminate \( 2m \) from the left, we use the subtraction property of equality.

Step2: Evaluate each option

• Subtract 5 from both sides: This moves the constant term, not the \( m \)-term. Not helpful for moving \( m \)-terms.
• Add \( 2m \) to both sides: This would add \( 2m \) to the right, increasing the \( m \)-terms there, but the left would have \( 4m \), not eliminating the \( m \)-term from the left.
• Subtract \( 2m \) from both sides: Subtracting \( 2m \) from both sides gives \( 5 + 2m - 2m=7m - 2m \), simplifying to \( 5 = 5m \), which moves all \( m \)-terms to the right.

Now, to find \( m \):

Step3: Solve for \( m \)

From \( 5 = 5m \), divide both sides by 5: \( \frac{5}{5}=\frac{5m}{5} \), so \( m = 1 \).

Answer:

To move all \( m \)-terms to the right, we subtract \( 2m \) from both sides. The value of \( m \) is \( \boldsymbol{1} \).