Question
How many solutions will the equation 23(6m+9)−6=4m have?(1 point) Responses infinite/many solutions infinite/many solutions two solutions two solutions no solution no solution one solution
Answers
Answered by
GPT-4o mini
To determine how many solutions the equation \( 23(6m + 9) - 6 = 4m \) has, we can first simplify and solve the equation step by step.
1. Start by distributing the \( 23 \) on the left side:
\[
23(6m + 9) - 6 = 138m + 207 - 6 = 138m + 201
\]
So, the equation becomes:
\[
138m + 201 = 4m
\]
2. Next, we'll isolate the \( m \) terms by subtracting \( 4m \) from both sides:
\[
138m - 4m + 201 = 0
\]
This simplifies to:
\[
134m + 201 = 0
\]
3. Now, subtract \( 201 \) from both sides:
\[
134m = -201
\]
4. Finally, divide both sides by \( 134 \):
\[
m = -\frac{201}{134}
\]
This shows that there is exactly **one solution** to the equation.
Therefore, the answer is **one solution**.
1. Start by distributing the \( 23 \) on the left side:
\[
23(6m + 9) - 6 = 138m + 207 - 6 = 138m + 201
\]
So, the equation becomes:
\[
138m + 201 = 4m
\]
2. Next, we'll isolate the \( m \) terms by subtracting \( 4m \) from both sides:
\[
138m - 4m + 201 = 0
\]
This simplifies to:
\[
134m + 201 = 0
\]
3. Now, subtract \( 201 \) from both sides:
\[
134m = -201
\]
4. Finally, divide both sides by \( 134 \):
\[
m = -\frac{201}{134}
\]
This shows that there is exactly **one solution** to the equation.
Therefore, the answer is **one solution**.
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