Question

How many solutions will the equation 23(6m+9)−6=4m have?(1 point)
Responses

no solution
no solution

two solutions
two solutions

one solution
one solution

infinite/many solutions

Answer 1

To determine how many solutions the equation \( 23(6m + 9) - 6 = 4m \) has, let's simplify it step by step.

1. Start with the original equation:
\[
23(6m + 9) - 6 = 4m
\]

2. Distribute \( 23 \) on the left side:
\[
138m + 207 - 6 = 4m
\]

3. Simplify the left side:
\[
138m + 201 = 4m
\]

4. Subtract \( 4m \) from both sides:
\[
138m - 4m + 201 = 0
\]
which simplifies to:
\[
134m + 201 = 0
\]

5. Move \( 201 \) to the other side of the equation:
\[
134m = -201
\]

6. Solve for \( m \):
\[
m = -\frac{201}{134}
\]

Since we found a single value for \( m \), the equation has **one solution**.

Thus, the correct response is:

**one solution**.