Question

How many solutions will the equation 3 (6m + 9) - 6 = 4m have? (1 point)
• infinite/many solutions
• one solution
• no solution
• two solutions

Answer 1

To determine how many solutions the equation \( 3(6m + 9) - 6 = 4m \) has, we can simplify the equation step by step.

1. Distribute the 3 on the left side:
\[
3(6m + 9) = 18m + 27
\]
So the equation becomes:
\[
18m + 27 - 6 = 4m
\]

2. Simplify the left side:
\[
18m + 21 = 4m
\]

3. Next, isolate the variable \( m \) by moving all terms involving \( m \) to one side and constant terms to the other:
\[
18m - 4m = -21
\]
This simplifies to:
\[
14m = -21
\]

4. Now solve for \( m \):
\[
m = -\frac{21}{14} = -\frac{3}{2}
\]

Since we found one specific value for \( m \), the equation has **one solution**.

Thus, the answer is:
• one solution.