Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the number of solutions for the equation, we can solve it and see how many value(s) of m satisfy the equation.

First, let's simplify the equation:
2/3(6m + 9) - 6 = 4m
4m + 6 - 6 = 4m
4m = 4m

The equation simplifies to 4m = 4m, which is true for any value of m.

Therefore, the equation is an identity and will have infinitely many solutions.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the number of solutions for the equation 2/3(6m+9) - 6 = 4m, we need to solve the equation and check how many solutions it has.

Let's simplify the equation step by step:

1. Distribute the 2/3 to 6m+9: (2/3) * 6m + (2/3) * 9 - 6 = 4m
This simplifies to: 4m + 6 - 6 = 4m

2. Combine like terms: 4m = 4m
After subtracting 6 from both sides, we're left with: 4m = 4m

Now, we need to examine the equation 4m = 4m.

In this case, since the variable "m" appears on both sides of the equation and the coefficients are the same (4), the equation is an identity. This means that any value of "m" will satisfy the equation. Therefore, the equation has infinitely many solutions.

In summary, the equation 2/3(6m+9) - 6 = 4m has infinitely many solutions.

Answer 3

[AI-generated answer — Explain Bot]

To determine the number of solutions for the equation 2/3(6m+9)−6=4m, we need to solve the equation and see how many distinct solutions we obtain.

Step 1: Distribute the 2/3 to the terms inside the parentheses:
(2/3)(6m+9) − 6 = 4m
(4m + 6) − 6 = 4m

Step 2: Simplify the equation:
4m + 6 - 6 = 4m
4m = 4m

Step 3: Subtract 4m from both sides to isolate the variable:
4m - 4m = 0
0 = 0

Step 4: Analyze the result:
Since we obtained 0 = 0, this means that both sides of the equation are always equal, regardless of the value of m. Thus, no matter what value of m we choose, the equation remains true.

Therefore, the equation 2/3(6m+9)−6=4m has infinite solutions because any value of m will satisfy the equation.