Let's solve the equation step by step as you described. We're given the expression \( \frac{2}{1}(6x + 2) = 3x \).
Step 1: Distributing the \( \frac{2}{1} \) (which is just 2) to both terms inside the parentheses.
\[ 2(6x + 2) = 2 \cdot 6x + 2 \cdot 2 \]
Calculating each term:
- \( 2 \cdot 6x = 12x \)
- \( 2 \cdot 2 = 4 \)
So we can rewrite the equation as:
\[ 12x + 4 = 3x \]
Step 2: Rearranging the equation to isolate \( x \).
To isolate \( x \), we want to get all terms involving \( x \) on one side of the equation and the constant terms on the other side.
Subtract \( 3x \) from both sides:
\[ 12x + 4 - 3x = 3x - 3x \]
This simplifies to:
\[ 12x - 3x + 4 = 0 \]
Which further simplifies to:
\[ 9x + 4 = 0 \]
Step 3: Solving for \( x \).
Now, we need to isolate \( x \). First, subtract 4 from both sides:
\[ 9x = -4 \]
Now divide both sides by 9:
\[ x = -\frac{4}{9} \]
Solution:
The solution to the equation \( \frac{2}{1}(6x + 2) = 3x \) is
\[ x = -\frac{4}{9} \]