To determine how many solutions the equation has, we will first simplify it step by step. The given equation is:
\[ 6x = \frac{6}{1} (36x + 6). \]
This can be simplified to:
\[ 6x = 6 \cdot (36x + 6). \]
Now, we'll distribute the 6 on the right side:
\[ 6x = 216x + 36. \]
Next, we'll get all terms involving \( x \) on one side and the constant terms on the other side. We can move \( 216x \) to the left side by subtracting \( 216x \) from both sides:
\[ 6x - 216x = 36. \]
This simplifies to:
\[ -210x = 36. \]
Now, we can solve for \( x \) by dividing both sides by \( -210 \):
\[ x = \frac{36}{-210} = -\frac{6}{35}. \]
Since we found a single value for \( x \), the equation has one solution.
Final answer:
One solution.
1 answer