Question

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

one solution
one solution

infinite/many solutions
infinite/many solutions

no solution
no solution

two solutions

Answer 1

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

1. Distribute \( 23 \) on the left side:
\[
23 \times 6m + 23 \times 9 - 6 = 4m
\]
This simplifies to:
\[
138m + 207 - 6 = 4m
\]
\[
138m + 201 = 4m
\]

2. Next, we'll move \( 4m \) to the left side:
\[
138m - 4m + 201 = 0
\]
This simplifies to:
\[
134m + 201 = 0
\]

3. Now, isolate \( m \):
\[
134m = -201
\]
\[
m = -\frac{201}{134}
\]

Since we found a unique value for \( m \), we conclude that the equation has exactly one solution.

The answer is:
**one solution**.