- Analyze the operations applied to \(m\): subtraction by 2 followed by division by 3.
- Identify the inverse operations: multiplication by 3 to undo division, then addition by 2 to undo subtraction.
- Determine the correct first step by reversing the order of operations: multiply both sides of the equation by 3.
- The correct choice is: \(\boxed{\text{Multiply both sides by 3}}\).
Explanation
- Analyzing the equation structure
To isolate the variable \(m\) in the equation \(\frac{m-2}{3} = 7\), we need to reverse the operations applied to \(m\). Looking at the structure of the left-hand side, \(m\) is first subtracted by 2, and the resulting value is then divided by 3. To isolate \(m\), we must reverse these operations in the opposite order of how they were applied. The last operation performed on \(m\) was dividing by 3, so the first step in reversing the process is to perform the inverse operation, which is multiplication. Therefore, we should multiply both sides of the equation by 3.
- Executing the first step
By multiplying both sides of the equation \(\frac{m-2}{3} = 7\) by 3, we clear the denominator on the left side:
\[ \left( \frac{m-2}{3} \right) \times 3 = 7 \times 3 \]
\[ m - 2 = 21 \]
Now, the equation is much simpler. To finish isolating \(m\), we would add 2 to both sides, resulting in \(m = 23\). The question asks for the first step, which is multiplying both sides by 3.
Examples
Think of solving an equation like solving a puzzle or untying a knot. If you tied a rope in a specific sequence—perhaps first folding it, then knotting it—you must reverse these actions in the exact opposite order to untie it. Here, the variable \(m\) has had operations "tied" to it in a specific order: first subtraction, then division. To "untie" it, you must first undo the division by multiplying, and then undo the subtraction by adding. This step-by-step approach ensures you systematically isolate the variable while keeping both sides of the equation balanced.