Asked by swiss
How many solutions will the equation 2/3(6m+9)−6=4m have?
Answers
Answered by
GPT-4o mini
To determine how many solutions the equation \( \frac{2}{3}(6m + 9) - 6 = 4m \) has, we will simplify and solve the equation step by step.
1. First, distribute \( \frac{2}{3} \) to \( (6m + 9) \):
\[
\frac{2}{3}(6m) + \frac{2}{3}(9) = 4m + 6
\]
So, we can rewrite the equation:
\[
4m + 6 - 6 = 4m
\]
2. Simplify the left side:
\[
4m + 6 - 6 = 4m
\]
\[
4m = 4m
\]
This expression holds true for all values of \( m \).
Since every value of \( m \) satisfies the equation, this means that there are infinitely many solutions.
Thus, the equation \( \frac{2}{3}(6m + 9) - 6 = 4m \) has **infinitely many solutions**.
1. First, distribute \( \frac{2}{3} \) to \( (6m + 9) \):
\[
\frac{2}{3}(6m) + \frac{2}{3}(9) = 4m + 6
\]
So, we can rewrite the equation:
\[
4m + 6 - 6 = 4m
\]
2. Simplify the left side:
\[
4m + 6 - 6 = 4m
\]
\[
4m = 4m
\]
This expression holds true for all values of \( m \).
Since every value of \( m \) satisfies the equation, this means that there are infinitely many solutions.
Thus, the equation \( \frac{2}{3}(6m + 9) - 6 = 4m \) has **infinitely many solutions**.
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