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

two solutions
two solutions

no solution

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
11 days ago

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

1. Distribute the \( 23 \):
\[
23(6m) + 23(9) - 6 = 4m
\]
This becomes:
\[
138m + 207 - 6 = 4m
\]

2. Combine the constant terms:
\[
138m + 201 = 4m
\]

3. Now, isolate the \( m \) terms on one side:
\[
138m - 4m + 201 = 0
\]
This simplifies to:
\[
134m + 201 = 0
\]

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

Since we found one specific value for \( m \), there is **one solution** to the equation.

Thus, the correct response is:
**one solution**.