Question

How many solutions will the equation 2/3(6m+9)−6=4m have?(1 point)
Responses

Answer 1

To determine how many solutions the equation \( \frac{2}{3}(6m+9) - 6 = 4m \) has, we will first simplify and solve it step-by-step.

Starting with the equation:

\[
\frac{2}{3}(6m + 9) - 6 = 4m
\]

Step 1: Distribute \( \frac{2}{3} \) to the terms inside the parentheses.

\[
\frac{2}{3} \cdot 6m + \frac{2}{3} \cdot 9 - 6 = 4m
\]

This simplifies to:

\[
4m + 6 - 6 = 4m
\]

Step 2: Simplify the left side:

\[
4m = 4m
\]

Now we see that both sides of the equation are identical, meaning that the equation is true for all values of \( m \).

**Conclusion:** Since this is a true statement for all \( m \), the equation has an infinite number of solutions.

So, the answer is: **infinitely many solutions.**