What is the value of x in the equation Negative two-thirds x + 9 = four-thirds x minus 3?

Answer 1

To solve the equation \(-\frac{2}{3}x + 9 = \frac{4}{3}x - 3\), we can follow these steps:

1. Move all terms involving \(x\) to one side and constants to the other side.

   Start by adding \(\frac{2}{3}x\) to both sides:

   \[ 9 = \frac{4}{3}x + \frac{2}{3}x - 3 \]

   This simplifies to:

   \[ 9 = \left(\frac{4}{3} + \frac{2}{3}\right)x - 3 \]

   Combining the fractions on the right:

   \[ 9 = \frac{6}{3}x - 3 \]

   This simplifies to:

   \[ 9 = 2x - 3 \]

2. Isolate \(2x\) by adding \(3\) to both sides:

   \[ 9 + 3 = 2x \]

   This simplifies to:

   \[ 12 = 2x \]

3. Solve for \(x\) by dividing both sides by \(2\):

   \[ x = \frac{12}{2} = 6 \]

So, the value of \(x\) is \(\boxed{6}\).