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

Question

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, let's simplify and solve it step by step.

1. Start with the equation: $$23(6m+9)-6=4m$$

2. Distribute $23$ on the left side: $$138m+207-6=4m$$ Simplifying this gives: $$138m+201=4m$$

3. Next, isolate $m$ by subtracting $4m$ from both sides: $$138m-4m+201=0$$ Which simplifies to: $$134m+201=0$$

4. Now, isolate $m$: $$134m=-201$$ $$m=-\frac{201}{134}$$

Since we arrived at a single value of $m$, this means there is exactly one solution to the equation.

Thus, the answer is:

one solution