How many solutions will the following equation have?

Question

2(2m+3)−6=4m
2
(
2
𝑚
+
3
)
−
6
=
4
𝑚

(1 point)
Responses

No solution
No solution

Infinite/many solutions
Infinite/many solutions

One solution
One solution

Two solutions

Answer 1

To find the solutions to the equation \( 2(2m + 3) - 6 = 4m \), let's simplify the left side step by step:

1. Distribute the 2: \[ 2(2m + 3) = 4m + 6 \]

2. Substitute this back into the original equation: \[ 4m + 6 - 6 = 4m \]

3. Simplify: \[ 4m = 4m \]

At this point, we can see that the equation \( 4m = 4m \) is always true for any value of \( m \). This indicates that there are infinitely many solutions since every value of \( m \) satisfies the equation.

Thus, the answer is: Infinite/many solutions.