Question

solve x to determine if the equation has one, none, infinite

9 (x + 1) = 3 (5x + 1) - 12

Answer 1

To solve the equation \( 9 (x + 1) = 3 (5x + 1) - 12 \), we can start by simplifying both sides.

1. Distribute the terms on both sides:
\[
9x + 9 = 15x + 3 - 12
\]
Simplifying the right side:
\[
9x + 9 = 15x - 9
\]

2. Now, let's isolate \( x \). First, subtract \( 9x \) from both sides:
\[
9 = 15x - 9x - 9
\]
This simplifies to:
\[
9 = 6x - 9
\]

3. Next, add \( 9 \) to both sides:
\[
9 + 9 = 6x
\]
Thus we have:
\[
18 = 6x
\]

4. Finally, divide both sides by \( 6 \):
\[
x = 3
\]

The solution \( x = 3 \) indicates that the equation has **one unique solution**.