Question

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

no solution
no solution

infinite/many solutions
infinite/many solutions

two solutions
two solutions

one solution

Answer 1

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

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

2. Move all terms involving \(m\) to one side and constants to the other:
\[
138m - 4m = -201
\]
\[
134m = -201
\]

3. Divide both sides by \(134\):
\[
m = -\frac{201}{134}
\]

Since we have derived a unique value for \(m\), the equation has **one solution**.

Therefore, the answer is:
**one solution**.