Question How many solutions will the equation \frac{2}{3}\left(6m+9\right)-6=4m have?(1 point) Responses infinite/many solutions infinite/many solutions two solutions two solutions one solution one solution no solution no solution

Answer 1

To determine the number of solutions for the equation \(\frac{2}{3}(6m + 9) - 6 = 4m\), we will first simplify the left side of the equation.

1. Distribute \(\frac{2}{3}\): \[ \frac{2}{3}(6m) + \frac{2}{3}(9) - 6 \] This simplifies to: \[ 4m + 6 - 6 \] which further simplifies to: \[ 4m \]

2. Now we have the equation: \[ 4m = 4m \]

This equation is true for all values of \(m\) since both sides are identical.

Thus, there are infinite solutions to the equation.

The correct response is: infinite/many solutions.