To determine how many solutions the equation \( 23(6m + 9) - 6 = 4m \) has, we first simplify the equation.
Starting with the original equation:
\[ 23(6m + 9) - 6 = 4m \]
Distributing \( 23 \) inside the parentheses:
\[ 138m + 207 - 6 = 4m \]
This simplifies to:
\[ 138m + 201 = 4m \]
Now, we'll isolate \( m \) by moving all \( m \) terms to one side:
\[ 138m - 4m + 201 = 0 \]
This simplifies to:
\[ 134m + 201 = 0 \]
Next, we isolate \( m \):
\[ 134m = -201 \]
Then, dividing both sides by \( 134 \):
\[ m = -\frac{201}{134} \]
This equation has only one solution for \( m \).
Thus, the answer is:
one solution.
1 answer