Question

Solve for x
to determine if the equation has one, none, or infinite solutions.

9(x+1)=3(5x+1)−12

Answer 1

To determine if the equation \( 9(x + 1) = 3(5x + 1) - 12 \) has one, none, or infinite solutions, let's first simplify both sides of the equation.

1. Start by expanding both sides of the equation:
\[
9(x + 1) = 9x + 9
\]
\[
3(5x + 1) - 12 = 15x + 3 - 12 = 15x - 9
\]

So, the equation becomes:
\[
9x + 9 = 15x - 9
\]

2. Next, let's rearrange the equation by moving all \( x \) terms to one side and constant terms to the other side:
\[
9 + 9 = 15x - 9x
\]
\[
18 = 6x
\]

3. Now, we can solve for \( x \):
\[
x = \frac{18}{6} = 3
\]

Now that we have found \( x = 3 \), we can conclude that the equation has one solution.

Final answer: The equation has **one solution**: \( x = 3 \).